Find the quadratic polynomial, the sum and product of whose zeros are −3   and 2   respectively.

# Find the quadratic polynomial, the sum and product of whose zeros are   and   respectively.

1. A
${{x}}^{{2}}{+}{3}{x}{+}{2}$
2. B
${{x}}^{{2}}{+}{3}{x}{-}{2}$
3. C
${{x}}^{{2}}{-}{3}{x}{-}{2}$
4. D
${{x}}^{{2}}{-}{3}{x}{+}{2}$

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### Solution:

Given that the sum of zeroes and product of zeroes of a quadratic polynomial is   and   respectively. We need to find the quadratic polynomial.
A quadratic polynomial is of the form
Let us assume the zeroes of the polynomial be
Based on the relationship between zeroes and polynomials we have quadratic polynomial as:

Now we have,

Substituting the values in equation (i) we have,

Hence, the quadratic polynomial is  .
Therefore, option 1 is correct.

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