Question

If the discriminant is zero in a quadratic formula, determine the number of real solutions for that quadratic formula. Please help.

Answer 1

Keywords

discriminant, quadratic equation, real solution

we know that

The formula to calculate the solutions of the quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}$

where

The discriminant of the quadratic equation  is equal to

$b^{2}-4ac$

in this problem we have  that

$b^{2}-4ac=0$

so

substitute in the formula

$x=\frac{-b(+/-)\sqrt{0}}{2a}$

$x=-\frac{b}{2a}$  -------> is one real solution

therefore

The answer is

one real solution

Answer 2

The discriminant gives the type of solutions that will be found for a

quadratic equation.

The number of real solutions for the quadratic formula is one.

Reasons:

If the discriminant in the quadratic formula, y = a·x² + b·x + c, is the value;

$\mathbf{b^{2}-4\cdot a\cdot c}}\ \ in \ x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$

Where;

a, b, and c are real numbers, we have

A zero discriminant gives;

$x = \dfrac{-b\pm \sqrt{0}}{2\cdot a} = \dfrac{-b\pm0}{2\cdot a} = \dfrac{-b}{2\cdot a}$

Therefore;

$x = \dfrac{-b}{2\cdot a}$

$\dfrac{-b}{2\cdot a}$ is one real number

Therefore;

The number of real solutions for the quadratic formula is one.

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