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Find a
polynomial P(x) of 2nd degree if P(1)=0
P (2) 3
P(-3)=0​

1 Answer

6 votes

Given:

P(x) is a 2nd degree polynomial.


P(1)=0,\ P(2)=3,\ P(-3)=0

To find:

The polynomial P(x).

Solution:

If P(x) is a polynomial and P(c)=0, then c is a zero of the polynomial and (x-c) is a factor of polynomial P(x).

We have,
P(1)=0,\ P(-3)=0. It means 1 and -3 are two zeros of the polynomial P(x) and (x-1) and (x+3) are two factors of the polynomial P(x).

So, the required polynomial is defined as:


P(x)=a(x-1)(x+3) ...(i)

Where, a is a constant.

We have,
P(2)=3. So, substituting
x=2,\ P(x)=3 in (i), we get


3=a(2-1)(2+3)


3=a(1)(5)


3=5a


(3)/(5)=a

Putting
a=(3)/(5) in (i), we get


P(x)=(3)/(5)(x-1)(x+3)

Therefore, the required polynomial is
P(x)=(3)/(5)(x-1)(x+3).

User Underfrog
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