Question

If the equation $2x^4+7x^3+ax+b=0$ 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
• B. a = 11, b = - 6
• C. a = 12, b = - 5
• D. a = 12, b = 5

Answer 1

The correct option is B

a = 11, b = - 6

$(x-1)$ and $(x-3)$ exactly divides the expression $2x^4+7x^3+ax+b$

Using factor theorem:
for $x=1$,

$2-7+a+b=0$

$\Rightarrow a+b=5$ _____ (1)

and for $x=3$,

162 - ( 7 × 27 ) + 39 + b = 0

$3a+b=-27$ _____ (2)

Solving equation (1) and (2)

we get,

$a=11,b=-6.$