The polynomials ax3 – 7x2 + 7x – 2 and x3 – 2ax2 + 8x – 8 when divided by x – 2, leave the same remainder. Find
the value of a.
Answers
Answer:
a=10
Step-by-step explanation:
Let f(x)=2x
3
−7x
2
+ax−6
Put x−2=0
⇒x=2
When f(x) is divided by (x−2), remainder =f(2)
∴f(2)=2(2)
3
−7(2)
2
+a.2−6
=2.8−7.4+2a−6
=16−28−6+2a
=2a−18
Let g(x)=x
3
−8x
2
+(2a+1)x−16
when g(x) is divided by (x−2) remainder =g(2)
∴g(2)=(2)
3
−8(2)
2
+(2a+1)2−16
=8−32+4a+2−16
=4a−38
By the condition we have
f(2)=g(2)
2a−18=4a−38
4a−2a=38−18
2a=20
a=
2
20
a=10
∴ Thus, the value of a=10
ANSWER⤵
a=10
Step-by-step explanation:⤵
Let f(x)=2x
3
−7x
2
+ax−6
Put x−2=0
⇒x=2
When f(x) is divided by (x−2), remainder =f(2)
∴f(2)=2(2)
3
−7(2)
2
+a.2−6
=2.8−7.4+2a−6
=16−28−6+2a
=2a−18
Let g(x)=x
3
−8x
2
+(2a+1)x−16
when g(x) is divided by (x−2) remainder =g(2)
∴g(2)=(2)
3
−8(2)
2
+(2a+1)2−16
=8−32+4a+2−16
=4a−38
By the condition we have
f(2)=g(2)
2a−18=4a−38
4a−2a=38−18
2a=20
a=
2
20
a=10
∴ Thus, the value of a=10