Question

answer it guys ..............​

Answer 1

What are a and b if x=0, and x=-1 are the roots of the polynomial g(x) =2x³-3x²+ax+b?

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STEP 1.

When we say that x=0 and x=-1 are “the roots of the polynomial g(x)” we mean that when x=0 or x=-1, g(x)=0. So let’s start by replacing x with those values of x.

g(0) = 2(0)³ -3(0)² +a(0) +b = 0

g(-1) = 2(-1)³ -3(-1)² +a(-1) +b = 0

STEP 2.

Simplify each of those equations by multiplying.

g(0) = 0 -0 +0 +b = 0

g(-1) = -2 -3 -a +b = 0

STEP 3.

Simplify each of those equations by adding.

g(0) = b = 0

g(-1) = -5 -a +b = 0

STEP 4.

In the first equation b=0. Replace with b with 0 in the second equation and simplify.

g(-1) = -5 -a +0 = 0

g(-1) = -5 -a = 0

a=-5

So a=-5, b=0, and g(x) = 2x³ -3x² -5x +0

HOPE IT HELPS............

Answer 2

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