Find a quadratic polynomial, the sum and product of whose zeroes are −7   and −18   respectively. Also find the zeroes.

# Find a quadratic polynomial, the sum and product of whose zeroes are   and   respectively. Also find the zeroes.

1. A
polynomial   and zeroes
2. B
polynomial   and zeroes
3. C
polynomial   and zeroes
4. D
polynomial   and zeroes

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### Solution:

Given that the sum and product of the zeroes of a polynomial are   and  respectively. We need to find the quadratic polynomial and its zeroes.
General form of quadratic polynomial is given as:
In splitting the middle term method we split the middle term of quadratic equation in   and   such that,
middle term
product of first and third term
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,

Equating the values in equation (i) we have,

Now equating   we have,

Hence, the quadratic polynomial is  .
Using the splitting the middle term approach, on the polynomial  , we have,
Hence, the zeroes of the polynomial are
Therefore, the quadratic polynomial is   and the zeroes are
Therefore, option 2 is correct.

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