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

1, 1

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#### Solution

1, 1

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

Given α + ß = `–b/a = 1`

αß = `c/a = 1`

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

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

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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