Question

if x=0 and x=-1 are the roots of polynomial f(x)= 2x3 -3x3 + ax + b, find the value of a and b ( 9th rd Sharma, ch polynomial, ex 6.2, level 2)​

Answer 1

Correct equation

$\implies\rm 2x^{3}-3x^{2} +ax+b$

Solution

⇒ at x =0

we get

$\rm2\times0^{3} -3\times0^{2} + a\times0+b=0$

$\rm0-0+0+b=0\\ b=0\:\:\:\:......(i)$

⇒at x = -1

we get

$\to\rm2\times(-1)^{3} -3\times(-1)^{2} + a\times-1+b=0\\ \to-2-3-a+b=0\\\to-5-a+b=0\\\to a-b=-5 \:\:\:\:\:\:\: .....(ii)$

now put the value of b on ii eq

⇒a - b = -5

⇒a - 0 = -5

⇒a = -5

answer:- a = - 5 and b = 0