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 ๐Ÿ’ฌ

 

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?

two

Which function has a negative discriminant value?

1 Expert Answer

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 b2 โˆ’ 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 b2 – 4ac > 0, the graph has two real solutions. If b2 – 4ac = 0, the graph has one real solution. If b2 – 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 ax2 + bx + c = 0, the discriminant is b2 โˆ’ 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc โˆ’ 4b3 โˆ’ 4a3c โˆ’ 27c2.

How do you factor a quadratic equation?

With the quadratic equation in this form:
  1. Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.
  2. Step 2: Rewrite the middle with those numbers:
  3. 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, bยฒ-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 b2 โ€“ 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, b2 โˆ’4ac = (โˆ’3)2โˆ’ 4 ยท 1 ยท 4 = 9 โˆ’ 16 = โˆ’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: ax2 + bx + c. The discriminant, D = b2 – 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 b2 โ€“ 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?

For the general equation axยฒ+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 โ‰  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 ฮ”=b2โˆ’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 ฮ”โ‰ฅ0, the expression under the square root is non-negative and therefore roots are real.

How does the discriminant determine the nature of the roots?

For the general equation axยฒ+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?

ax2 + bx + c = 0 is the equation of a parabola. The discriminant is b2 – 4ac, which you find in the quadratic formula: x = [-bยฑโˆš(b2-4ac)]/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 b24ac, which is defined for any quadratic equation ax2 + bx + c = 0. If 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.