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# If Ax2 + Bx + C = 0 Has Equal Roots, Then C = - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

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

• $\frac{- b}{2a}$

• $\frac{b}{2a}$

• $\frac{- b^2}{4a}$

• $\frac{b^2}{4a}$

#### Solution

The given quadric equation is ax2 + bx + c = 0 , and roots are equal

Then find the value of c.

Let  alpha = beta be two roots of given equation

Then, as we know that sum of the roots

alpha + beta = (-b)/ a

alpha + alpha = (-b)/ a

2alpha = (-b)/ (2a)

alpha = (-b)/ (2a)

And the product of the roots

alpha. beta = c/a

alpha alpha = c / a

Putting the value of alpha

(-b)/(2a) xx (-b)/(2a) = c/a

b^2/4a = c

Therefore, the value of c = (b^2)/(4a).

Is there an error in this question or solution?

#### APPEARS IN

Solution If Ax2 + Bx + C = 0 Has Equal Roots, Then C = Concept: Solutions of Quadratic Equations by Factorization.
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