Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

Find te values of a and b so that x^4+ x^3+ 8x^2+ax+b is divisible by x^2+1.
Asked by | 13 May, 2012, 11:52: AM
answered-by-expert Expert Answer

Since x 2 + 1 divides x 4 + x 3 + 8x 2 + ax + b , so the quotient will be a polynomial of degree 2.

So, we can write

x 4 + x 3 + 8x 2 + ax + b = (x 2 + 1) (a 1 x 2 + b 1 x + c 1)

? x 4 + x 3 + 8x 2 + ax + b = a 1 x 4 + a 1 x 2 + b 1 x 3 + b 1 x + c 1 x 2 + c 1

? x 4 + x 3 + 8x 2 + ax + b = a 1 x 4 + b 1 x 3 + (a 1 + c 1) x 2 + b 1 x + c 1

Comparing the coefficient of x 4 on both sides, we get –

a 1 = 1

On comparing the coefficient of x 3, we get –

b 1 = 1

On comparing the coefficient of x 2, we get –

a 1 + c 1 = 8

? 1 + c 1 = 8

? c 1 = 7

On comparing the coefficient of x on both sides, we get –

a = b 1 = 1

? a = 1

On comparing the constants on both sides, we get –

b = c 1 = 7

? b = 7

Answered by | 13 May, 2012, 04:05: PM
CBSE 10 - Maths
Asked by anubhutiupadhaya | 14 Mar, 2024, 11:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by reetudetha | 08 Jan, 2024, 04:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by mysticsurya201 | 04 Jan, 2024, 08:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by fatehbahadurtiwari3 | 30 Dec, 2023, 06:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by dhaneswarnimal80 | 11 Nov, 2023, 06:50: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by skandachiranjeevin | 01 Nov, 2023, 08:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by sazimkhan178 | 16 Sep, 2023, 11:27: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by pranavtamboli65 | 09 Jul, 2023, 09:13: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by rekhapreetham | 15 Jun, 2023, 08:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by dimpaldihingia2 | 24 May, 2023, 06:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×