For what values of a is 2 x3-a x2-11 x-a-3 exactly divisible by 2 x-1

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Byju's Answer

Standard IX

Mathematics

Factor Theorem

For what valu...

Question

For what values of a is 2x³+ax²+11x+a+3 exactly divisible by 2x-1

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Solution

2x - 1 must be a factor of the given polynomial.
One of the roots must be x = 1/2

Plug in x = 1/2, and equate the polynomial to zero:
2(1/2)^3 + a(1/2)^2 + 11(1/2) + a + 3 = 0
1/4 + a/4 + 11/2 + a + 3 = 0
5a/4 + 35/4 = 0
5a + 35 = 0
a = -7

SOLUTION: 2x^3 - 7x^2 + 11x - 4 is exactly divisible by 2x - 1

Check: (x^2 - 3x + 4)(2x - 1) = 2x^3 - 7x^2 + 11x - 4

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For what values of a is 2x3+ax​​​​​2+11x+a+3 exactly divisible by 2x-1

For what values of a is 2x³+ax²+11x+a+3 exactly divisible by 2x-1