Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

`-1/4 ,1/4`

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#### Solution

`-1/4 ,1/4`

Let the quadratic polynomial be *ax*^{2} + *bx* + *c*, and its zeroes be α + ß

Given α + ß = `-1/4 = –b/a`

αß = `1/4 = c/a`

If *a* = 4, b = 1, *c* = 1

Therefore, the quadratic polynomial is 4*x*^{2} + *x* +1.

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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