Question

If the polynomials p(x) = x^4

+ ax^3 + 9x^2 + 5ax + 5 and q(x) = x4^

- 2x^3 + 3ax^2 + 40x – 47.when divided by (x-2)

Leave the same remainder. find the value of ‘a​

Answer 1

Step-by-step explanation:

It is given that a polynomial ax3−3x2+4 when divided by (x−2) leaves the remainder p. Let us substitute x=2 in ax3−3x2+4 and equate it to p as follows:

a(2)3−3(2)2+4=p⇒(a×8)−(3×4)+4=p⇒8a−12+4=p⇒8a−8=p....(1)

Similarly, given a polynomial 2x3−5x+a when divided by (x−2) leaves the remainder q. Let us substitute x=2 in 2x3−5x+a and equate it to q as follows:

2(2)3−(5×2)+a=q⇒(2×8)−10+a=q⇒16−10+a=q⇒6+a=q....(2)

It is also given that p−2q=4, we, now substitute the values of p and q from equations 1 and 2 as shown below:

p−2q=4⇒8a−8−2(6+a)=4⇒8a−8−12−2a=4⇒