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If 2 is a Root of the Quadratic Equation 3 X 2 + P X − 8 = 0 and the Quadratic Equation 4 X 2 − 2 P X + K = 0 Has Equal Roots, Find the Value of K. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

Question

If 2 is a root of the quadratic equation $3 x^2 + px - 8 = 0$ and the quadratic equation $4 x^2 - 2px + k = 0$  has equal roots, find the value of k.

Solution

The given quadratic equation is $3 x^2 + px - 8 = 0$ and one root is 2.

Then, it satisfies the given equation.

$3 \left( 2 \right)^2 + p\left( 2 \right) - 8 = 0$

$\Rightarrow 12 + 2p - 8 = 0$

$\Rightarrow 2p = - 4$

$\Rightarrow p = - 2$

The quadratic equation  $4 x^2 - 2px + k = 0$,has equal roots.

Putting the value of p, we get

$4 x^2 - 2( - 2)x + k = 0$

$\Rightarrow 4 x^2 + 4x + k = 0$

Here,
$a = 4, b = 4 \text { and } c = k$.
As we know that
$D = b^2 - 4ac$
Putting the values of $a = 4, b = 4 \text { and } c = k$.

$D = \left( 4 \right)^2 - 4\left( 4 \right)\left( k \right)$

$= 16 - 16k$

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

Thus,

$16 - 16k = 0$

$\Rightarrow 16k = 16$

$\Rightarrow k = 1$

Therefore, the value of k is 1.

Is there an error in this question or solution?

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Solution If 2 is a Root of the Quadratic Equation 3 X 2 + P X − 8 = 0 and the Quadratic Equation 4 X 2 − 2 P X + K = 0 Has Equal Roots, Find the Value of K. Concept: Solutions of Quadratic Equations by Factorization.
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