Question

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

`0, sqrt5`

Answer 1

`0, sqrt5`

Let the polynomial be ax² + bx + c, and its zeroes be α and ß

Given α + ß = 0 = `–b/a`

αß = `sqrt5 ` = `c/a`

If a = 1, b = 0, c = `sqrt5`

Therefore, the quadratic polynomial is x² + `sqrt5`

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