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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

ConceptSolutions of Quadratic Equations by Factorization

#### 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?

#### APPEARS IN

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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