Which equation has the solutions x is equal to 1 plus or minus square root of 5 ?

The two solutions are 1 + √5 and 1 − √5. Their sum is 2 and their product is 1 − 5 = −4. A monic quadratic with these roots is x² − (sum)x + product = x² − 2x − 4, which is choice D.

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