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The Value of C for Which the Equation Ax2 + 2bx + C = 0 Has Equal Roots is - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

Question

The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is

• $\frac{b^2}{a}$

• $\frac{b^2}{4a}$

• $\frac{a^2}{b}$

• $\frac{a^2}{4b}$

Solution

The given quadric equation is ax2 + 2bx + c = 0 , and roots are equal

Then find the value of c.

Let alpha and beta  be two roots of given equation alpha = beta

Then, as we know that sum of the roots

alpha + beta = (-2b)/a

alpha + alpha = (-2b)/a

2alpha = (-2b)/a

alpha = (-b)/a

And the product of the roots

alpha . beta = c/a

alpha alpha = c /a

Putting the value of alpha

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

b^2/a = c

Therefore, the value of  c =b^2/a

Is there an error in this question or solution?

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Solution The Value of C for Which the Equation Ax2 + 2bx + C = 0 Has Equal Roots is Concept: Solutions of Quadratic Equations by Factorization.
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