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If x2+x-12 divides p(x) = x3+x2+bx-84 …

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If x2+x-12 divides p(x) = x3+x2+bx-84 exactly. Find a and b

Posted by Rohit Roy 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 7 months ago

X2+x-12 =0
x2+ 4x-3x-12=0
x(x+4)-3(x+4)=0
(x-3) (x+4) =0
so x= 3
or. x=-4

p(x)÷g(x)= q(x) + r
p(x)÷g(x)= q(x) +0
x3 + ax2 + bx -84 ÷ x2+x-12
after dividing remainder will be ax2 - x2+bx+12x-84=0
let x=3
27a-9+3b+36-84=0
9a + 3b= 57
3(3a+b)=57
3a+b=19________eq 1
now let x= -4
ax2-x2+bx+12x-84=0
16a-16-4b-48-84=0
16a-4b=148
4(4a-b)=148
4a-b=37_________eq 2
add equation 1 and equation 2
so ,
3a + b +4a -b = 19+37
7a = 56
a= 8
put a=8 in equation 1
3a+b = 19
24 +b=19
or b=-5

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