Question

If -1,1 & 3 are the zeroes of a cubic polynomial, which of the following is the correct expression of the polynomial?

• A. $x^3+3x^2-x+3$
• B. $x^3-3x^2+x+3$
• C. $x^3-3x^2-x-3$
• D. $x^3-3x^2-x+3$
  

Answer 1

The correct option is D $x^3-3x^2-x+3$

We know that if a cubic polynomial is $a{x}^3+b{x}^2+cx+d$, then

Sum of zeroes =$-\frac{b}{a}$
Sum of zeroes taken two at a time =$\frac{c}{a}$
Product of zeroes =$-\frac{d}{a}$

Assume a = 1
$-\frac{b}{a}=-b-1+1+3=3$
$\frac{c}{a}=c$
$=(-1)\left(1\right)+\left(1\right)\left(3\right)+\left(3\right)(-1)$
$=-1+3-3=-1$
$-\frac{d}{a}=-d=(-1)\left(1\right)\left(3\right)=-3$

Therefore b = -3, c = -1, d = 3

Hence, the cubic polynomial will be $x^3-3x^2-x+3$