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If (x-6) is a factor of …

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If (x-6) is a factor of x³+ ax²+bx-b =0 and a-b = 7 find the value of a and b

Posted by Abhishek Raj 8 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Dharmendra Kumar 8 years, 5 months ago

Since (x-6) is a factor of x³+ax²+bx-b=0------(1)

Therefore x=6 is one of the roots of the given cubic polynomial.

So put x=6 in eq.(1) we get,

6³+a×6²+b×6-b=0

216+36a+6b-b=0

36a+5b=-216 -------(2)

given that a-b=7

a=7+b -----(3)

Substituting the value of a from eq.(3) into eq.(2) we get

36(7+b)+5b=-216

252+36b+5b=-216

41b=-216-252

41b=-468

{tex}b = {-468 \over 41}{/tex}

Substituting this value in eq.(3) we get

a=7+({tex}{-468\over 41}){/tex}={tex}{41×7-468\over 41}{/tex}={tex}{287-468 \over 41}{/tex}={tex}{-181\over 41}{/tex}

4Thank You

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