Question

If a Monic cubic polynomial has roots 2,3 and 5 then the coefficient of x is given by
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Answer 1

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A cubic polynomial P(x) is such that P(1)=1, P(2)=2, P(3)=3 and P(4)=5. The value of P(6) is:

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VIDEO EXPLANATION

ANSWER

Given P(1)=1,P(2)=2,P(3)=3,P(4)=5

Let f(x)=(P(x)−x)

f(1)=P(1)−1=1−1=0

f(2)=P(2)−2=2−2=0

f(3)=P(3)−3=3−3=0

∴f(x)=0,x=1,2,3

⇒f(x)=a(x−1)(x−2)(x−3)

P(x)=a(x−1)(x−2)(x−3)+x

Put x=4

5=a(3)(2)(1)+4

⇒a=

6

1

∴P(x)=

6

1

(x−1)(x−2)(x−3)+x

∴P(6)=

6

1

(5)(4)(3)+6=16