Question

if (x - 2) and (x + 3) are factors of x ^ 3 + a * x ^ 2 + bx - 30 , find a and b.

Answer 1

Step-by-step explanation:

Given (x + 2) is a factor of x³ + ax + b

⇒ (−2)³ + a(-a) + b = 0 (x + 2 = 0 →

x = -2)

⇒-8-2a+b=0 ⇒-2a + b 8.... (1)

=

Also,given that (x+ 3) is a factor of x³ + ax + b

⇒ (−3)³ + a(−3) + b = 0

⇒-27 3a+b=0

⇒ −3a + b = 27 ...(2)

Subtracting (1) from (2) we have

-a 19⇒a=-19

Substituting a = -19 in (1), we have

-2 × (-19) + b = 8

⇒ 38+ b = 8

⇒b=-30

Answer 2

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