Question

Find the remainder of the following quadratic equation if one of the zeroes is -2. x³ - 4x² + 7=0

A. 11
B. 15
C. 23
D. 13​

Answer 1

Answer:

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Class 9

>>Maths

>>Polynomials

>>Remainder Theorem

>>Find the values of a and b ...

Question

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Find the values of a and b so that x

4

+x

3

+8x

2

+ax+b is divisible by x

2

+1.

Hard

Solution

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Let us first divide the given polynomial x

4

+x

3

+8x

2

+ax+b by (x

2

+1) as shown in the above image:

From the division, we observe that the quotient is x

2

+x+7 and the remainder is (a−1)x+(b−7).

Since it is given that x

4

+x

3

+8x

2

+ax+b is exactly divisible by x

2

+1, therefore, the remainder must be equal to 0 that is:

(a−1)x+(b−7)=0

⇒(a−1)x+(b−7)=0⋅x+0

⇒(a−1)=0,(b−7)=0(Bycomparingcoefficients)

⇒a=1,b=7

Hence, a=1 and b=7.