Latest SSC Aptitude Question SOLUTION: if for the two real constants a and b the expression a*x^3+3*x^2+8*x+b is exactly divisible by (x+2) and (x-2) then value of a and b ???

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if for the two real constants a and b the expression a*x^3+3*x^2+8*x+b is exactly divisible by (x+2) and (x-2) then value of a and b ???

Asked In SSC mohan (12 years ago)

Solved Chetan Anand Read Solution (3)

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Chetan Anand  (12 years ago)

Ans: a=-2 & b=-12

Substituting the value of x=2 and x=-2 in the given equation leads us to following two equation having solution(other equation obtained has no solution)
8a+b=-28 & 8a-b=-4
Solving these two equations, we get,
a=-2 and b=-12

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Amit kumar  (11 years ago)

a*x^3+3*x^2+8*x+b this equation have three roots,
let roots are -2, 2 and p
sum of product of two roots at a time = 8/a
=> -2*2+2*p-2*p=8/a
=> -4= 8/a
=> a= -2
replace x---> 1/x, the equation becomes b*x^3+8*x^2+3*x+a have roots 1/2, -1/2 and 1/p,
sum of product of two roots at a time = 3/b
=> (1/2)(-1/2)+(1/2)(1/p)+(-1/2)(1/p) = 3/b
=> -1/4= 3/b
=> b = -12

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Rakesh Kumar Kohli  (12 years ago)

Ans. a= -2, b= -12
(x+2)(x-2)(-2x+3)= (x^2-4)(-2x+3)= -2x^3+8*x+3x^2-12, giving a= -2, b= -12

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