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

`1/4 , -1`

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#### Solution

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

Given α + ß = `1/4 = –b/a`

αß = -1 = `c/a`

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

The quadratic polynomial is 4*x*^{2} – *x* -4.

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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