Question

Find a quadratic polynomial whose zeros are -1/4 and 1/4

Answer 1

(x+1/4)(x-1/4)=0

x^2-1/16=0

16x^2-1=0

Answer 2

The quadratic polynomial whose zeros are -1/4 and 1/4 is:

$16x^2-1=0$

Solution:

Given that,

We have to find the quadratic polynomial whose zeros are -1/4 and 1/4

$\frac{-1}{4} \text{ and } \frac{1}{4}$

The quadratic equation is given as:

$x^2 - ( \text{ sum of zeros})x + \text{ product of zeros } = 0$

Find the sum of zeros

$\text{sum of zeros } = \frac{-1}{4} + \frac{1}{4}= 0$

Find the product of zeros

$\text{product of zeros } = \frac{-1}{4} \times \frac{1}{4} = \frac{-1}{16}$

Therefore,

$x^2 -0x -\frac{1}{16} = 0\\\\x^2 - \frac{1}{16} = 0\\\\16x^2 - 1 = 0$

Thus the equation is found

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