when 4x^3-ax^2+bx-4 is divided by x-2 and x+1 the respective remainders are 20 and -13.
find values of A and B
Answers
Answer:
.
MATHS
If the expression ax
4
+bx
3
−x
2
+2x+3 has remainder 4x+3 when divided by x
2
+x−2, then the value of a and b, is
December 20, 2019avatar
Manita Edge
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ANSWER
As x
2
+x−2=(x+2)(x−1)
Let f(x)=ax
4
+bx
3
−x
2
+2x+3=(x
2
+x−2)Q(x)+4x+3, where Q(x) is the quotient
Then,
f(−2)=a(−2)
4
+b(−2)
3
−(−2)
2
+2(−2)+3=4(−2)+3
⇒16a−8b−4−4+3=−5⇒2a−b=0 ......... (1)
And
f(1)=a+b−1+2+3=4(1)+3⇒a+b=3 ........ (2)
Solving (1) and (2) simultaneously, we get
a=1,b=2
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