If a polynomial $x^{4} - 5 x^{3} + x^{2} + k x - 12$ is exactly divisible by $x^{2} - 5 x + 4$ , then find the value of k.

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Solution

$f a c t o r o f x^{2} - 5 x + 4 = (x - 1) (x - 4) h e n c e x = 1 a n d 4 a r e z e r o o f g i v e n p o l y n o m i a l ∴ P (1) = 01 - 5 + 1 + k - 12 = 0 o r k = 12 + 3 = 15 a n d P (4) = 0 256 - 320 + 16 + 4 k - 12 = 0 4 k = + 60 ∴ k = 15$

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If a polynomial x4−5x3+x2+kx−12 is exactly divisible by x2−5x+4, then find the value of k.

factorofx2−5x+4=(x−1)(x−4)hencex=1and4arezeroofgivenpolynomial∴P(1)=01−5+1+k−12=0ork=12+3=15andP(4)=0256−320+16+4k−12=04k=+60∴k=15

If a polynomial $x^{4} - 5 x^{3} + x^{2} + k x - 12$ is exactly divisible by $x^{2} - 5 x + 4$ , then find the value of k.

$f a c t o r o f x^{2} - 5 x + 4 = (x - 1) (x - 4) h e n c e x = 1 a n d 4 a r e z e r o o f g i v e n p o l y n o m i a l ∴ P (1) = 01 - 5 + 1 + k - 12 = 0 o r k = 12 + 3 = 15 a n d P (4) = 0 256 - 320 + 16 + 4 k - 12 = 0 4 k = + 60 ∴ k = 15$