If x^2 + x - 2 is the G.C.D of the expressions (x - 1)(2x^2 + ax + 2) and (x + 2) 3x^2 + bx + 1), then the values of a and b respectively are
a) - 5, - 4
b) 5, - 4
c) - 5, 4
d) 4, 5
Answers
Answer:
If (x+2) is the HCF of the polynomials (x-4) (2x^2+x-a) and (x+1) (2x^2+bx-12), then what is the value of 5a-6b?
f1(x)=(x−4)(2x2+x−a)
f2(x)=(x+1)(2x2+bx−12)
since(x+2)isHCFx=−2isarootoff1andf2
f1(−2)=0
→−6(6−a)=0
→a=6
f2(−2)=0
→−1(−4−2b)=0
→b=−2
so , 5a−6b=42
If (x+2) is GCD of
P(x)=(x-4)(2x^2+x-a) then
P(-2)=0
(2–4)(2×4–2-a)=0
(6-a)=0
a=6
If (x+2) is HCF of
G(x)=(x+1)(2x^2-bx-12) then
G(-2)=0
(-2+1){2×4-b×(-2)-12}=0
-4–2b=0
b=-2
5a-6b=5×6–6×(-2)=30+12=42
If (x+2) is the HCF of the polynomials (x-4) (2x^2+x-a) and (x+1) (2x^2+bx-12), then what is the value of 5a-6b?
f1(x)=(x−4)(2x2+x−a)
f2(x)=(x+1)(2x2+bx−12)
since(x+2)isHCFx=−2isarootoff1andf2
f1(−2)=0
→−6(6−a)=0
→a=6
f2(−2)=0
→−1(−4−2b)=0
→b=−2
so , 5a−6b=42
If (x+2) is GCD of
P(x)=(x-4)(2x^2+x-a) then
P(-2)=0
(2–4)(2×4–2-a)=0
(6-a)=0
a=6
If (x+2) is HCF of
G(x)=(x+1)(2x^2-bx-12) then
G(-2)=0
(-2+1){2×4-b×(-2)-12}=0
-4–2b=0
b=-2
5a-6b=5×6–6×(-2)=30+12=42