The **discriminant** is negative, so the equation has two non-real solutions. **If the discriminant** is a **perfect square**, then the solutions to the equation are **not** only real, but also rational. **If the discriminant** is positive but **not a perfect square**, then the solutions to the equation are real but irrational.

Then, What if the discriminant is less than zero?

**If the discriminant** of a quadratic function is **less than zero**, that function has no real roots, and the parabola it represents does not intersect the x-axis.

Considering this, What is the discriminant calculator? The **discriminant calculator** is a free online tool that gives the **discriminant** value for the given coefficients of a quadratic equation. BYJU’S online **discriminant calculator** tool makes the calculations faster and easier where it displays the value in a fraction of seconds.

**21 Related Questions and Answers Found ?**

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**What if the discriminant is not a perfect square?**

The **discriminant** is negative, so the equation has two non-real solutions. **If the discriminant** is a **perfect square**, then the solutions to the equation are **not** only real, but also rational. **If the discriminant** is positive but **not a perfect square**, then the solutions to the equation are real but irrational.

**How do you know if a discriminant is rational?**

The **discriminant** is 0, so the equation has a double root. **If the discriminant** is a perfect square, then the solutions to the equation are not only real, but also **rational**. **If the discriminant** is positive but not a perfect square, then the solutions to the equation are real but irrational.

**How many solutions does a negative discriminant have?**

**Which function has a negative discriminant value?**

But if the graph does NOT touch the x-axis, then there are no real solutions, which means that the **discriminant is negative**. So you are looking for a graph that does NOT touch the x-axis. A **has** a y **value** less than zero (-1) and opens up, so it must cross the x-axis.

**What is a repeated real number solution?**

**REPEATED SOLUTIONS**. When the left side factors into two linear equations with the same **solution**, the quadratic equation is said to have a **repeated solution**. We also call this **solution** a root of multiplicity 2, or a double root.

**Why is B 2 4ac called the discriminant?**

It is **called the Discriminant**, because it can “**discriminate**” between the possible types of answer: when **b ^{2}** −

**4ac**is positive, we get two Real solutions. when it is zero we get just ONE real solution (both answers are the same) when it is negative we get a pair of Complex solutions.

**What is the axis of symmetry?**

The graph of a quadratic function is a parabola. The **axis of symmetry** of a parabola is a vertical line that divides the parabola into two congruent halves. The **axis of symmetry** always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the **axis of symmetry** of the parabola.

**How do you prove that a quadratic equation is always positive?**

The graph of a quadratic equation that has a negative discriminant is the one that never intersect **x-axis**. The graph of a quadratic equation that has a zero discriminant is the one that intersect **x-axis** at only one point.

**How do you graph a discriminant?**

The **discriminant** shows you the type and number of solutions of the **graph**. If b^{2} – 4ac > 0, the **graph** has two real solutions. If b^{2} – 4ac = 0, the **graph** has one real solution. If b^{2} – 4ac < 0, the **graph** has two imaginary solutions.

**What is the discriminant in algebra?**

mathematics. **Discriminant**, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax^{2} + bx + c = 0, the **discriminant** is b^{2} − 4ac; for a cubic equation x^{3} + ax^{2} + bx + c = 0, the **discriminant** is a^{2}b^{2} + 18abc − 4b^{3} − 4a^{3}c − 27c^{2}.

**How do you factor a quadratic equation?**

**With the quadratic equation in this form:**

- Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.
- Step 2: Rewrite the middle with those numbers:
- Step 3: Factor the first two and last two terms separately:

**What is the discriminant of an equation?**

The **discriminant** is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the **equation** has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.

**What does a negative discriminant tell you?**

**What to do if the discriminant is negative?**

This relationship is always true: **If** you **get** a **negative** value inside the square root, then there **will** be no real number solution, and therefore no x-intercepts. In other words, **if** the the **discriminant** (being the expression b^{2} – 4ac) has a value which is **negative**, then you won’t have any graphable zeroes.

**What is the value of the discriminant of F?**

Notice that the **discriminant of f**(x) is negative, b^{2} −4ac = (−3)^{2}− 4 · 1 · 4 = 9 − 16 = −7. is the x-coordinate of the vertex of a parabola. Thus, a parabola has exactly one real root when the vertex of the parabola lies right on the x-axis.

**How do you tell if an equation has no real solution?**

The constants are the numbers alone with **no** variables. **If** the coefficients are the same on both sides then the sides will not equal, therefore **no solutions** will occur. Use distributive property on the right side first.

**What is a discriminant value?**

A **discriminant** is a **value** calculated from a quadratic equation. It use it to ‘discriminate’ between the roots (or solutions) of a quadratic equation. A quadratic equation is one of the form: ax^{2} + bx + c. The **discriminant**, D = b^{2} – 4ac. Note: This is the expression inside the square root of the quadratic formula.

**What to do if the discriminant is negative?**

This relationship is always true: **If** you **get** a **negative** value inside the square root, then there **will** be no real number solution, and therefore no x-intercepts. In other words, **if** the the **discriminant** (being the expression b^{2} – 4ac) has a value which is **negative**, then you won’t have any graphable zeroes.

**How do you find roots of an equation?**

The **roots** of any quadratic **equation** is given by: x = [-b +/- sqrt(-b^2 – 4ac)]/2a. Write down the quadratic in the form of ax^2 + bx + c = 0. If the **equation** is in the form y = ax^2 + bx +c, simply replace the y with 0. This is done because the **roots** of the **equation** are the values where the y axis is equal to 0.

**How do you prove that a quadratic equation is always positive?**

**equation**ax²+bx+c,

As the discriminant is negative, the **quadratic equation** has no real root. And if we put x=0, then the **equation** will be 5 which is **positive** so the **equation** totally lies above the real axis. So the sign of the **equation** is same as the sign of a i.e **positive**.

**What is the discriminant calculator?**

A **real** number x will be called a **solution** or a root if it satisfies the equation, meaning . It is easy to see that the roots are exactly the x-intercepts of the quadratic function. , that is the intersection between the **graph** of the quadratic function with the x-axis.

**How do you find the sign of a quadratic equation?**

When x be real then, the **sign** of the **quadratic** expression ax^2 + bx + c is the same as a, except when the roots of the **quadratic equation** ax^2 + bx + c = 0 (a ≠ 0) are real and unequal and x lies between them.

**How does the discriminant determine the nature of the roots?**

The **discriminant** is defined as Δ=b2−4ac. This is the expression under the square **root** in the quadratic formula. The **discriminant** determines the **nature of the roots** of a quadratic equation. If Δ≥0, the expression under the square **root** is non-negative and therefore **roots are** real.

**How does the discriminant determine the nature of the roots?**

**equation**ax²+bx+c,

As the discriminant is negative, the **quadratic equation** has no real root. And if we put x=0, then the **equation** will be 5 which is **positive** so the **equation** totally lies above the real axis. So the sign of the **equation** is same as the sign of a i.e **positive**.

**What is quadratic equation in math?**

In **math**, we define a **quadratic equation** as an **equation** of degree 2, meaning that the highest exponent of this function is 2. The standard form of a **quadratic** is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of **quadratic equations** include all of these: y = x^2 + 3x + 1.

**Which is the graph of a quadratic equation that has a negative discriminant?**

Answer: The correct graph is D. then the graph will intersect the **x-axis** in one point. then the graph won’t intersect the **x-axis** because it will not have real roots.

**What is the axis of symmetry?**

The graph of a quadratic function is a parabola. The **axis of symmetry** of a parabola is a vertical line that divides the parabola into two congruent halves. The **axis of symmetry** always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the **axis of symmetry** of the parabola.

**How do you find the discriminant of a graph?**

ax^{2} + bx + c = 0 is the equation of a parabola. The **discriminant** is b^{2} – 4ac, which you **find** in the quadratic formula: x = [-b±√(b^{2}-4ac)]/2a. The **discriminant** shows you the type and number of solutions of the **graph**.

**What are real solutions on a graph?**

Answer: The correct graph is D. then the graph will intersect the **x-axis** in one point. then the graph won’t intersect the **x-axis** because it will not have real roots.

**What does B 2 4ac tell you?**

The discriminant **is** the expression **b ^{2}** –

**4ac**, which

**is**defined for any quadratic equation ax

**+ bx + c = 0. If**

^{2}**you**get 0, the quadratic will have exactly one solution, a double root. If

**you**get a negative number, the quadratic will have no real solutions, just two imaginary ones.

**What is the value of the discriminant for the quadratic equation?**

A **real** number x will be called a **solution** or a root if it satisfies the equation, meaning . It is easy to see that the roots are exactly the x-intercepts of the quadratic function. , that is the intersection between the **graph** of the quadratic function with the x-axis.