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

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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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