Question

find the value of a and b so that x⁴+6x³+9x²+ax+b is exactly divisible by x²+3​

Answer 1

$\bold \red{answer}$

Given that x²+3 divides exactly the polynomial

x⁴+6x³+9x²+ax+b

⇒x²+3 is a factor of x⁴+6x³+9x²+ax+b

⇒ by factor theorem, the Remainder=0

⇒(a−9)x+b=0

⇒a−9=0 and b=0

∴a=9,b=0