A quadratic polynomial whose zeros are 3 and 4

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Find the quadratic polynomial whose zeros are 3 and -4

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Answer:

The obtained polynomial is x^2+x-12 having zeroes as 3 and -4.

To find:

Quadratic polynomial

Solution:

Given : Zeros of quadratic polynomial are 3 and -4.

Sum of zeros = 3 + (-4)  = -1

Product of zeros = (3)(-4) = -12

Now the required polynomial is  

\begin{array} { c } { x ^ { 2 } + ( \text {product of zeros} ) - x ( \text {sum of zeros} ) } \\\\ { = x ^ { 2 } + ( - 12 ) - x ( - 1 ) } \\\\ { = x ^ { 2 } - 12 + x } \\\\ { = x ^ { 2 } + x - 12 } \end{array}

Thus, the obtained polynomial is x^2+x-12 having zeroes as 3 and -4.


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