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If the Equation Ax2 + 2x + a = 0 Has Two Distinct Roots, If - CBSE Class 10 - Mathematics

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Question

If the equation ax2 + 2x + a = 0 has two distinct roots, if

  • a = ±1

  • a = 0

  • a = 0, 1

  • a = −1, 0

Solution

The given quadric equation is ax2 + 2x + a = 0 , and roots are distinct.

Then find the value of a.

Here, a = a,b = 2 and, c = a

As we know that `D = b^2 - 4ac`

Putting the value of a = a,b = 2 and, c = a

`= (2)^2 - 4 xx a xx a`

`= 4 - 4a^2`

The given equation will have real and distinct roots, if D > 0

`4 -4a^2 = 0`

       `4a^2 = 4`

         ` a^2 = 4/4`

           `a = sqrt1`

             `= ± 1`

Therefore, the value of ` a = ± 1`.

  Is there an error in this question or solution?

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Solution If the Equation Ax2 + 2x + a = 0 Has Two Distinct Roots, If Concept: Solutions of Quadratic Equations by Factorization.
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