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What happens if the discriminant is 0?

Asked by: Dalius Mieth

asked in category: General Last Updated: 5th March, 2020

What happens if the discriminant is 0?

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

In respect to this, what happens 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.

Additionally, when discriminant is zero then roots are? When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.

In this regard, how many solutions are there if the discriminant is zero?

one solution

How do you prove a quadratic has no real roots?

If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots. x2 – 5x + 2. If the discriminant is greater than zero, this means that the quadratic equation has no real roots. Therefore, there are no real roots to the quadratic equation 3x2 + 2x + 1.

38 Related Question Answers Found

How many roots if discriminant is negative?

This all comes directly from the quadratic formula. If the discriminant is positive, then you have , which leads to two real number answers. If it’s negative, you have , which gives two complex results. And if b2 – 4ac is 0, then you have , so you have only one solution.

How many real roots does a polynomial have?

If we count roots according to their multiplicity (see The Factor Theorem), then: A polynomial of degree n can have only an even number fewer than n real roots. Thus, when we count multiplicity, a cubic polynomial can have only three roots or one root; a quadratic polynomial can have only two roots or zero roots.

What is a real root?

Given an equation in a single variable, a root is a value that can be substituted for the variable in order that the equation holds. In other words it is a “solution” of the equation. It is called a real root if it is also a real number. For example: x2−2=0.

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 many roots can a quadratic equation have?

A quadratic equation with real coefficients can have either one or two distinct real roots, or two distinct complex roots. In this case the discriminant determines the number and nature of the roots. There are three cases: If the discriminant is positive, then there are two distinct roots.

How do you solve a discriminant?

a) Given. Find the discriminant Δ = b 2 – 4ac. For the equation to have one solution, the discriminant has to be equal to zero. The equation m 2 – 4 = 0 has two solutions. b) For the equation to have 2 real solution, the discriminant has to be greater than zero. The inequality m 2 – 4 > 0 has the following solution set.

What does a negative discriminant mean?

A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

What is a 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 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2.

What can the discriminant tell you?

The discriminant tells us the following information about a quadratic equation: If the solution is a real number or an imaginary number. If the solution is rational or if it is irrational. If the solution is one unique number or two different numbers.

How many solutions would a quadratic equation have if the discriminant is 12?

If the discriminant of a quadratic equation is 12 , then it has two distinct real roots. Note that 12 is not a perfect square, so if the coefficients of the quadratic are integers or otherwise rational, then the roots are both irrational.

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