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If the Equation 9x2 + 6kx + 4 = 0 Has Equal Roots, Then the Roots Are Both Equal to - CBSE Class 10 - Mathematics

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Question

If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to

  • \[\pm \frac{2}{3}\]

  • \[\pm \frac{3}{2}\]

  • 0

  • ±3

Solution

The given quadric equation is 9x2 + 6kx + 4 = 0, and roots are equal.

Then find roots of given equation.

Here,  a = 9, b = 6k and , c = 4

As we know that  `D = b^2 - 4ac`

Putting the value of  a = 9, b = 6k and , c = 4

` = (6k)^2 - 4 xx 9 xx 4`

` = 36k^2 - 144`

The given equation will have equal roots, if D = 0

  `36k^2 - 144 = 0`

  `36(k^2 - 4) = 0`

         `k^2 - 4 = 0`

` k^2 = 4`

  `k = ±2`

So, putting the value of k in quadratic equation

When k = 2then equation be and when  k = -2 then

  `9x^2 + 6xx 2x + 4 = 0`

       `9x^2 + 12x + 4 = 0`

`9x^2 + 6x xx 6x + 4 = 0`

`3x (3x + 2) + 2 (3x + 2) = 0`

and

         `9x^2 + 6x - 2x + 4 = 0`

                `9x^2 - 12x + 4 = 0`

         `9x^2 - 6x - 6x + 4 = 0`

`3x (3x - 2) - 2 (3x - 2) = 0`

Therefore, the value of  `x  = ± 2/3`.

  Is there an error in this question or solution?

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Solution If the Equation 9x2 + 6kx + 4 = 0 Has Equal Roots, Then the Roots Are Both Equal to Concept: Solutions of Quadratic Equations by Factorization.
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