How do I form a quadratic equation when only its two roots are given?

When the roots are given, use the standard form x² − (sum of roots)x + (product of roots) = 0. First find the sum and the product of the two given roots. For roots 3 and −5, the sum is 3 + (−5) = −2 and the product is 3 × (−5) = −15. Substitute these in: x² − (−2)x + (−15) = 0, which simplifies to x² + 2x − 15 = 0. You can verify by factorising: (x + 5)(x − 3) = 0 gives roots −5 and 3, which is correct. This method always works, just be careful with the signs of the sum, because the formula has a minus before the sum term.