Q.14
The polynomials ax'-3.rº + 4 and 2.r-5.x + a when divided by (x - 2) leave the remainder
p and q respectively. If p - 2q = 4. find the value of a
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It is given that a polynomial ax
3
−3x
2
+4 when divided by (x−2) leaves the remainder p. Let us substitute x=2 in ax
3
−3x
2
+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 2x
3
−5x+a when divided by (x−2) leaves the remainder q. Let us substitute x=2 in 2x
3
−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
⇒6a−20=4
⇒6a=4+20
⇒6a=24
⇒a=
6
24
⇒a=4
Hence, a=4.
Step-by-step explanation:
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