Question

Find the values of a and b so that the polynomial x4+ax3-7x2+8x+b is exqctly divisible by x+2as wellas x+3

Answer 1

Hi ..dear..here is your solution....

Answer 2

put x=-2 in the equation
$16 - 8a - 28 - 16 + b = 0 \\ - 8a + b = 28$
put x= -3
$81 - 27a - 63 - 24 + b = 0 \\ - 27a + b = 6$
subtract both equations
$19a = 22 \\ a = \frac{22}{19}$
now solve for b
$- 8 \times \frac{22}{19} + b = 28 \\ b = 28 + \frac{176}{19}$
$b = \frac{ 532+ 176}{19} \\ b = \frac{708}{19}$
is the answer