Question

plz answer this fastly

Answer 1

Answer:

Alpha = 3, Beta = 8. In following question alpha is represented by 'a' and beta by 'b'.

Step-by-step explanation:

Given (x+1), (x+2) are factors of polynomial x^3+3x^2-2ax+b

a=? ,b=?

Let p(x)=x^3+3 x^2-2ax+b

By factor theorem

p(-1)=(-1)^3+3(-1)^2-2a(-1)+b=0

-1+3+2a+b=0

-2+2a+b=0

2a+b=2

2a=2-b ➡(1)

p(-2)=(-2)^3+3(-2)^2-2a(-2)+b=0

-8+12+4a+b=0

4+4a+b=0

4+2(2a)+b=0

4+2(2-b)+b=0 [since from (1)]

4+4-2b+b=0

8-b=0

b=8

Substitute b=8 in eq-(1)

2a=2-b

2a=2-8

2a=-6

a=-3

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Hope it helps.....