Find the quadratic polynomial with the given numbers as the sum and product of its zeroes: $\frac{1}{4},\ -1$.
Given: Sum and product of the zeroes of the quadratic polynomial are: $\frac{1}{4},\ -1$.
To do: To find the required quadratic polynomial.
Solution:
Sum of the zeroes$=\frac{1}{4}$
Product of the zeroes$=-1$
The quadratic polynomial is:
$x^2+(sum\ of\ the\ zeroes)x + product\ of\ the\ zeroes=0$
$\Rightarrow x^2+( \frac{1}{4})x+( -1)=0$
$\Rightarrow 4x^2+x-1=0$
Thus, the required polynomial is $4x^2+x-1=0$.
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