Question

When the polynomial 2x3 + 3x2 + 3x – a is divided by x2 – 1, the remainder is 5x + b, then the value of under root a+b+6 is

Answer 1

Step-by-step explanation:

Given:

when polynomial 2x³+3x²+3x-a is divided by x²- 1 the remainder is 5x+ b.

To find: then value of √(a+b+6) is?

Solution: Divide 2x³+3x²+3x-a by x²-1

${x}^{2} - 1)2 {x}^{3} + 3 {x}^{2} + 3x - a(2x + 3 \\ 2 {x}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: - 2 {x} \: \: \: \: \: \: \: \: \: \: \: \\ ( - ) \: \: \: \: \: \: \: \: \: \: \: \: ( + ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - - - - \\ 3 {x }^{2} + 5x - a \\ 3 {x}^{2} \: \: \: \: \: \: \: \: \: - 3 \\ ( - ) \: \: \: \: \: \: \: \: \: \: \: ( + ) \: \: \: \: \: \\ - - - - - - - \\ 5x - a + 3\\ - - - - - - -$

Actually remainder is 5x-a+3

ATQ,remainder is 5x+b.

So, we can say that (on comparison both remainders)

b= -a+3

To find the value of √(a+b+6):

Put the value of b here

$\sqrt{a + b + 6 } = \sqrt{a - a + 3 + 6} \\ \\ \sqrt{a + b + 6 } = \sqrt{3 + 6} \\ \\ \sqrt{a + b + 6 } = \sqrt{9} \\ \\ \bold{\red{\sqrt{a + b + 6 } = ±3}}$

Final answer:

Value of √(a+b+6)=±3

Hope it helps you.

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