Question

If sum and product of zeroes of a polynomial are ($-3$) and ($-2$) respectively, then a polynomial is

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

Hint:

Do not forget that any constant multiple $k(x^2 - Sx + P)$ is a valid polynomial with the same zeroes.
If your initial expression $x^2 + 3x - 2$ is not listed, try multiplying the entire expression by $-1$ to see if its negative counterpart is present!

Answer 1

The Correct Option is B

Step 1: Recall how sum and product of zeroes link to the coefficients.
For a quadratic $ax^2+bx+c$, the sum of zeroes is $-\frac{b}{a}$ and the product of zeroes is $\frac{c}{a}$. Instead of building the polynomial from scratch, we can test each option directly against the given sum $-3$ and product $-2$.
Step 2: Test option (B), $-x^2-3x+2$.
Here $a=-1$, $b=-3$, $c=2$. Sum of zeroes $= -\frac{b}{a} = -\frac{-3}{-1} = -3$, and product of zeroes $= \frac{c}{a} = \frac{2}{-1} = -2$. Both match the given values exactly.
Step 3: Confirm the other options fail.
Checking option (A) $x^2-3x-2$ gives sum $3$, product $-2$; option (C) gives sum $3$; option (D) gives sum $-3$ but product $2$. None of these match both conditions together, so option (B) is the only correct choice.
\[ \boxed{-x^2 - 3x + 2} \]