Question

if the polynomials x*3+ax*2+5 and x*3-2x*2+a are divided by (x+2) leavethe same remainder find the value of a​

Answer 1

Given

Polynomial x³+ax²+5 and x³−2x²+a divided by x+2 the remainder is same

Then x+2 = 0 or x = −2 replace x by −2 we get

⇒ p(x) = x³+ax²+5

⇒p(−2) = (−2)³+a(−2)²+5

⇒p(2) = −8+a×4+5

⇒P(2) = 4a−8+5

⇒p(2) = 4a−3

⇒q(x) = x³−2x²+a

⇒q(−2) = (−2)³−2(−2)²+a

⇒q(2) = −8−8+a

⇒A(2) = a−16

∴4a−3 = a−16

Subtract 'a' and add '3' both the sides

We get,

⇒4a−3−a+3 = a−16−a+3

⇒3a = −13

Divided both side by 3 we get

⇒ a = -13/3