the polynomial bx3+3x2-3 and 2x3-5x+b when divided by x-4 leave the reamainders R1 and R2 respectively Find the value - Maths - Polynomials - I

Question

the polynomial bx3+3x2-3 and
2x3-5x+b when divided by x-4 leave the reamainders
R1 and R2 respectively Find the value of b if
2R1 -R2=0

Ajanta Trivedi · Accepted Answer

let the given polynomial be $p (x) = b x^{3} + 3 x^{2} - 3 a n d q (x) = 2 x^{3} - 5 x + b$

when p(x) is divided by x-4 .remainder = p(4)

when q(x) is divided by x-4, remainder = q(4)

$R_{1} = p (4) R_{1} = b * 4^{3} + 3 * 4^{2} - 3 R_{1} = 64 b + 48 - 3 R_{1} = 64 b + 45 ......... (1) R_{2} = q (4) R_{2} = 2 * 4^{3} - 5 * 4 + b$

$R_{2} = 128 - 20 + b R_{2} = 108 + b ........... (2)$

given: $2 R_{1} - R_{2} = 0$

$2 (64 b + 45) - (108 + b) = 0 128 b + 90 - 108 - b = 0 127 b - 18 = 0 b = \frac{18}{127}$

hope this helps you.

cheers!!

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the polynomial bx3+3x2-3 and 2x3-5x+b when divided by x-4 leave the reamainders R1 and R2 respectively. Find the value of b if 2R1 -R2=0