Find the value of ‘k’ if x -1 is a factor of P(x) = 4 $x^{3}$ + $x^{2}$ – 3x + k.

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Solution

Since x-1 is the factor of 4 $x^{3}$ + $x^{2}$ – 3x + k, therefore at x = 1,

P(x) = 0

So 4 ${(1)}^{3}$ + ${(1)}^{2}$ – 3(1) + k = 0

i.e, 2 + k=0

and k = -2

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Q. Find the value of

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Find the value of ‘k’ if x -1 is a factor of P(x) = 4 $x^{3}$ + $x^{2}$ – 3x + k.

Find the value of k, if x − 1 is a factor of p(x) in each of the following cases:

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Find the value of k, if x - 1 is a factor p(x) in each of the following cases:
(i) $p (x) = x^{2} + x + k$
(ii) $p (x) = 2 x^{2} + k x + \sqrt{2}$
(iii) $p (x) = k x^{2} - \sqrt{2} x + 1$
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Q. Find the value of

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p (x) = k x^{2} - 3 x + k

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Find the value of ‘k’ if x -1 is a factor of P(x) = 4x3 + x2 – 3x + k.

Since x-1 is the factor of 4x3 + x2 – 3x + k, therefore at x = 1, P(x) = 0 So 4(1)3 + (1)2 – 3(1) + k = 0 i.e, 2 + k=0 and k = -2

Find the value of ‘k’ if x -1 is a factor of P(x) = 4 $x^{3}$ + $x^{2}$ – 3x + k.

Since x-1 is the factor of 4 $x^{3}$ + $x^{2}$ – 3x + k, therefore at x = 1,

P(x) = 0

So 4 ${(1)}^{3}$ + ${(1)}^{2}$ – 3(1) + k = 0

i.e, 2 + k=0

and k = -2