If the roots of equation are real and equal, then which of the following relation is true?

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Solution

Q.
If the roots of equation $a x^{2} + b x + c = 0, a \neq 0$ are real and equal, then which of the following relation is true

1 $a = \frac{b^{2}}{c}$

2 $b^{2} = a c$

3 $a c = \frac{b^{2}}{4}$

4 $c = \frac{b^{2}}{a}$

Ans.
(3)

If the discriminant is equal to zero, i.e., $b^{2} - 4 a c = 0$ where a, b, c are real numbers and $a \neq 0,$ then roots of the quadratic equation $a x^{2} + b x + c = 0,$ are real and equal $b^{2} - 4 a c = 0 \Rightarrow a c = \frac{b^{2}}{4}$

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