Question

If x2+x−2x2+x−2  is G.C.D of the expressions (x−1)(2x2+ax+2)(x−1)(2x2+ax+2)  and (x+2)(3x2+bx+1),(x+2)(3x2+bx+1),  then the values of a and b respectively are ​

Answer 1

Answer:

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

Step-by-step explanation:

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