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Question

If the equation 2x4+7x3+ax+b=0 has four real roots. Then find the value of a and b. Given that (x - 3) and (x - 1) may exactly divide the above given expression.


A

a = 6, b = - 11

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B

a = 12, b = 5

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C

a = 11, b = - 6

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D

a = 12, b = - 5

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Solution

The correct option is C

a = 11, b = - 6


(x1) and (x3) exactly divides the expression 2x4+7x3+ax+b

Using factor theorem:
for x=1,

27+a+b=0

a+b=5 _____ (1)

and for x=3,

162 - ( 7 × 27 ) + 39 + b = 0

3a+b=27 _____ (2)

Solving equation (1) and (2)

we get,

a=11,b=6.


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