Question

If (x – 6) is a factor of x3
+ ax2
+ bx – b = 0 and a – b = 7, find the values of a and b.

Answer 1

Answer:

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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 3 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Dharmendra Kumar 3 years, 9 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

b=−46841

Substituting this value in eq.(3) we get

a=7+(−46841)=41×7−46841=287−46841=−18141

Answer 2

Answer:

Step-by-step explanation:

Given that x - 6 is a factor of f(x). SO, substitute x =6 in the given polynomial equation

x^3+ax^2+bx-b = 0

put x = 6

6^3 + a (6^2) + 6b - b =0

216 + 36 a + 5b = 0

SO, 36 a + 5b = -216

also, given a - b = 7

so, 5a - 5b = 35

add these both equations

5b is cancelled

41 a = -181

so, a = -181/41 and b = -468/41

I hope it may helpfull to you

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