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# Find the Value of ‘K’ for Which X = 3 is a Solution of the Quadratic Equation (K + 2)X^2 - Kx + 6 = 0 - ICSE Class 10 - Mathematics

#### Question

Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation

(K + 2)x^2 - kx + 6 = 0

#### Solution

(K + 2)x^2 - Kx + 6 = 0     ...(1)

Substituting x = 3 in equation (1), we get

(K + 2) (3)^2 - K(3) + 6 = 0

:. 9(K +2) - 3K + 6 = 0

:. 9K + 18 - 3k + 6 = 0

:. 6k + 24 = 0

:. K= -4

Now, substituting K = –4 in equation (1), we get

(-4 + 2)x^2 - (-4)x + 6 = 0

:. -2x^2 + 4x + 6 = 0

:. x^2 - 2x - 3 = 0

:. x^2 -  3x + x - 3 = 0

:. x(x - 3) + 1(x- 3) = 0

:. (x + 1) (x + 3) = 0

So, the roots are x = –1 and x = 3.

Thus the other root of the equation is x = -1.

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#### APPEARS IN

2014-2015 (March) (with solutions)
Question 4.2 | 3.00 marks

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Solution Find the Value of ‘K’ for Which X = 3 is a Solution of the Quadratic Equation (K + 2)X^2 - Kx + 6 = 0 Concept: Quadratic Equations.
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