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