Question

if 2x+3 is a factor of the cubic polynomial p(x)=2x^3+9x^2-ax-b and a+b =16, then find the value of a and b.​

Answer 1

Answer:

$2x + 3 = 0 \\ 2x = - 3 \\ x = - \frac{3}{2}$

$p( \frac{ - 3}{2} ) = 2 {( \frac{ - 3}{2}) }^{3} + 9 {( \frac{ - 3}{2} )}^{2} - a( \frac{ - 3}{2} ) - b = 0 \\ \frac{ - 27}{4} + \frac{81}{4} + \frac{3a}{2} - b = 0 \\ \frac{81 - 27 + 6a - 4b}{4} = 0 \\ 54 + 6a - 4b = 0 \\ 6a - 4b = - 54 \\ 3a - 2b = - 27$

$3a - 2b = - 27 \\ 2a + 2b = 32 \\ - - - - - - - \\ 5a = 5 \\ a = 1$

(a+b)2=2a+2b

$a + b = 16 \\ 1 + b =16 \\ b = 16 - 1 \\ b = 15$

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