Find the value of k, if x – 1 is a factor of p(x) in the following case:-

p(x) = kx^{2} – 3x + k

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#### Solution

If *x* − 1 is a factor of polynomial *p*(*x*), then *p*(1) must be 0.

*p*(*x*) = *kx*^{2} − 3*x* + *k*

⇒ *p*(1) = 0

⇒ *k*(1)^{2} − 3(1) + *k* = 0

⇒ *k* − 3 + *k* = 0

⇒ 2*k *− 3 = 0

⇒ k = 3/2

Therefore, the value of* k *is 3/2.

Concept: Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.

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