Question

If ( x-2 ) and (x +3) are factors of x^3 + ax^2 + bx - 30, find a and b.
Give explanation step by step. ​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Expression x3 + ax2 + bx – 12

(x – 2) is a factor i.e., at x = 2 the remainder will be zero

⇒ (2)3 + a(2)2 + b(2) – 12 = 0

⇒ 8 + 4a + 2b – 12 = 0

⇒ 4a + 2b = 4

⇒ 2a + b = 2

When x + 3 is a factor i.e., at x = - 3 the remainder will be zero.

⇒ (- 3)3 + a(- 3)2 + b(- 3) – 12 = 0

⇒ - 27 + 9a – 3b – 12 = 0

⇒ 9a – 3b = 39

⇒ 3a – b = 13

Solving (i) and (ii) simultaneously

2a + b = 2

By adding 3a – b = 13

5a = 15

a = 3

Substituting the value of a in the equation (i)

⇒ 2 × 3 + b = 2

⇒ 6 + b = 2

⇒ b = 2 – 6 = - 4

⇒ a = 3, b = - 4