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CBSE Class 10 Answered

Find the values of  a and b so that x4 + x3 + 8x2 +ax + b is divisible by  4x2 + 3x – 2.
Asked by miniprasad | 04 May, 2018, 06:39: PM
answered-by-expert Expert Answer
According to the question,
Let a1x2 + b1x + c1 be the quotient when x4 + x3 + 8x2 +ax + b is divisible by 4x2 + 3x – 2.
x4 + x3 + 8x2 +ax + b = (4x2 + 3x – 2)(a1x2 + b1x + c1)
After simplifying we get
x4 + x3 + 8x2 +ax + b = 4a1x4 + 4b1x3 + 4c1x2 + 3a1x3 + 3b1x2 + 3c1x - 2a1x2 - 2b1x - 2c1
x4 + x3 + 8x2 +ax + b = 4a1x4 + (4b1 + 3a1)x3 + (4c1 + 3b1 - 2a1)x2 + (3c1 - 2b1) x - 2c1
Comparing coefficients on both sides we get,
 4a1 = 4 → a1 = 1
4b1 + 3a1 = 1  → 4b1 + 3 = 1 → b1 = -1/2
Similarly using 4c1 + 3b1 - 2a1 = 8 find c1 we get c1 = 23/8
Put the values of a1, b1, c1 in 3c1 - 2b1 = a and - 2c1 = b to find values of a and b.
Answered by Sneha shidid | 07 May, 2018, 09:35: AM

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