Question

ly. If y(x) = 4x+ (x - a), find g(x).
13. If the HCF of the polynomials f(x) = (x –2) (x2 + x - 4) and g(x) = (x2 - 5 x + 6) be
(x - 2), find the LCM of f(x) and g(x).
14. The HCF and ICM of two molimo​

Answer 1

Answer:

It is given that (x–4)(x−5) is the HCF of (x−5)(x

2

−x−a) and (x−4)(x

2

−2x−b), that is (x–4)(x−5) is a factor of both the polynomials.

Let f(x)=(x−5)(x

2

−x−a) and g(x)=(x−4)(x

2

−2x−b)

Now, f(x)=g(x) at x=4 and x=5.

Let us first substitute x=4 as shown below:

(4−5)(4

2

−4−a)=(4−4)(4

2

−2(4)−b)

⇒−1(16−4−a)=0(16−8−b)

⇒−1(12−a)=0

⇒a−12=0

⇒a=12

Now, we substitute x=5 as follows:

(5−5)(5

2

−5−a)=(5−4)(5

2

−2(5)−b)

⇒0(25−5−a)=1(25−10−b)

⇒0=25−10−b

⇒0=15−b

⇒b=15

Hence, a=12,b=15.

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