Question

Find the value of a+b if x-2 is a factor of ax2+3x+6 and 6x3-3x2-bx-4
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Answer 1

Answer:a=6 b=4Step-by-step explanation:x=2a×2+3(2)+6a×2+12a×2= -122a= -12a=12÷2a=66×3-3×2-b(2)-46×0×2-2b-4 12=2b+412-4=2b8=2b8÷2 =4b=4a+b =6+4 =10 is it corect

Answer 2

Given:-

• p(x) = ax² + 3x + 6
• f(x) = 6x³ - 3x² - bx - 4
• x - 2 is a factor of p(x) and f(x)

To find:-

• Value of a + b

Answer:-

From factor theorem, we know that (x - a) is a factor of a polynomial g(x) only if g(a) = 0.

As it is given that, (x - 2) is a factor of p(x) and f(x), that means p(2) = 0, and f(2) = 0

For p(x):

p(x) = ax² + 3x + 6

p(2) = (a * 2²) + (3 * 2) + 6 = 0

→ 4a + 6 + 6 = 0

→ 4a = -12

→ a = -3

For f(x):

f(x) = 6x³ - 3x² - bx - 4

→ f(2) = (6 * 2³) - (3 * 2²) - (b * 2) - 4 = 0

→ 48 - 12 - 2b - 4 = 0

→ 32 - 2b = 0

→ b = 16

Hence,

a + b = -3 + 16

→ a + b = 13 Ans