Question

6. If x=2 and a=0 are zemes of the polynomial p(x) 213-52? + ax +b. Find the values of 'a' and b. 2. 2x​

Answer 1

Answer:

If f(2)=2(2)

3

−5(2)

2

+a(2)+b=0

⇒16−20+2a+b=0⇒2a+b=4

⇒f(0)=2(0)

3

−5(0)

2

+a(0)+b=0

⇒b=0⇒2a=4⇒a=2,b=0

Answer 2

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If 0 and 1 are the zeroes of the polynomial f(x)=2x

3

−3x

2

+ax+b, find the values of a and b

Medium

Solution

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Given polynomial f(x)=2x

3

−3x

2

+ax+b is zero if x is 0 and 1

Replace x by 0 we get

2(0)

3

−3(0)

2

+a(0)+b=0

⇒0−0+0+b=0

⇒b=0

Replace x by 1 we get

2(1)

3

−3(1)

2

+a(1)+b=0

⇒2×1−3×1+a×1+b=0

⇒2−3+a+b=0

⇒−1+a+0=0 (Put the value of b=0)

⇒−1+a=0

Add 1 both side we get

−1+a+1=0+1

⇒a=1

Then a=1 and b=0