Question

If ax² + bx + c = 0 has equal roots, then c =
(a)$\frac{-b}{2a}$
(b)$\frac{b}{2a}$
(c)$\frac{-b^{2}}{4a}$
(d)$\frac{b^{2}}{4a}$

Answer 1

SOLUTION :  

Option (d) is correct :  b²/4a

Given : ax² + bx + c = 0

This given equation is the standard form of quadratic equation. Therefore, D(discriminant) = b² – 4ac

D = 0 (equal roots given)

b² – 4ac = 0

b² = 4ac  

c = b²/4a  

Hence, the value of c is b²/4a.

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Answer 2

If ax² + bx + c = 0 has equal roots, then c = ?

Answer : d) b² / 4a

Step by step explanation :

We know that :

Standard form of Quadratic equation : ax^2 + bx + c = 0

Here, a, b, c are real numbers and a is not equal to 0.

As per your question,

ax² + bx + c = 0 has equal roots.

Discriminant = D = b² - 4ac

.•. b² - 4ac = 0

Taking (-4ac ) to the R.H.S, it will become positive :

b² = 4ac  

Now, Taking 4a to the L.H.S, it will become :

b² / 4a = c

Thus, d) c = b² / 4a is the correct answer.