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

Question

asked Jul 23, 2022 94.6k views

1 Answer

Underfrog · Answer 1 · 2022-07-27T15:56:46+0000

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
.