Answer:
a = 2 ; b = 12
Explanation:
p(x)=x⁴ + ax³ - 7x² - 8x +b
p(x) is exactly divisible by (x + 2). So p(-2)=0
(-2)⁴ + a(-2)³ - 7(-2)² - 8(-2) +b = 0
16 - 8a - 7*4 +16 + b =0
16 - 8a - 28 + 16 + b =0
4 - 8a + b = 0
-8a + b = -4 -----------(i)
p(x) is exactly divisible by (x + 3). So p(-3)=0
(-3)⁴ + a(-3)³ - 7(-3)² - 8(-3) +b = 0
81 -27a - 63 + 24 + b =0
42 - 27a + b = 0
-27a + b = -42 ------------(ii)
-8a + b = -4 -----------(i)
-27a + b = -42 ------------(ii)
subtract 19a = 38
a = 38/19 = 2
a=2
Substitute a value in equation (i)
-8*2 + b= -4
-16 + b = -4
b = -4 + 16
b = 12