Math, asked by Anonymous, 8 months ago

If (x-1) and (x+2) are factor of p(x) = x^3 + 10x^2 + ax + b. find a & b

Answers

Answered by bhartijha41p8wy2m
2

Answer:

Let f(x) = x3 + 10x2 + ax + b

Since (x - 1) is a factor therefore

f(1) = 0

1 + 10 + a + b = 0

a + b = -11 … (1)

Also, (x + 2) is a factor, therefore

f(-2) = 0

(-2)3 + 10(-2)2 + a(-2) + b = 0

-8 + 40 -2a + b = 0

2a - b = 32 … (2)

Adding (1) and (2), we get

3a = 21

Or, a = 7

From (1), we get b = -11 - 7 = -18.

Hence, a = 7, b = -18.

Answered by nikitao4
0

Answer: A=-102.3 , b=203.3

Step-by-step explanation: p(x) = x^3+10x^2+ax+b.

 x-1 and x-2 are the factors of p(x).

let, x-1=0  and   x-2=0

     =) x=1  and   =) x=2

now, let , p(x)=1

therefore, p(1)=0

                  =)1^3+10×1^2+a×1+b=0

                  =)1^3+10^2+a+b=0

                  =)1+100+a+b=0

                   =)101+a+b=0

                     =)b=-101-a  

now,let, p(x) = 2

therefore,p(2)=0

               =)2^3+10×2^2+a×2+(-101-a)=0             [putting the value of b]

                =)2^3+20^2+2a-101+a=0

                =)8+400+3a-101=0

                  =) 408-101+3a=0

                 =)307+3a=0

                =)3a=-307

               =)a=-102.3

therefore, b=-101-(-102.3)

                   =-101+102.3

                    =203.3

hence, a=-102.3 and b=203.3

HOPE IT HELPS!

       

               

                       

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