Question

6. If 0 and 1 are the zeroes of the polynomial f(x)= 2x²-3x + ax+ b, is divided by (x - 2) leaves remainder 2, and (X + 2) leaves remainder -2. Find a and b.

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Answer 1

$*Question:-$

If 0 and 1 are the zeroes of the polynomial f(x)= 2x²-3x + ax+ b, is divided by (x - 2) leaves remainder 2, and (X + 2) leaves remainder -2. Find a and b.

$‡Answer:-$

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,

Hence the value of

• a = -5.
• b = 0 .