Which of these is a root of x² − 3x − 2 = 0?

Correct answer: a (3 − √17)/2

a = 1, b = −3, c = −2; b² − 4ac = 9 + 8 = 17; x = (3 ± √17)/2, one of which is (3 − √17)/2.

Why the other options are wrong

• b (−3 − √17)/2: Here −3 was used where −b = 3; it is a different quantity from the one asked for.
• c 1: Putting x = 1 gives 1 − 3 − 2 = −4, not 0.
• d 2: Putting x = 2 gives 4 − 6 − 2 = −4, not 0.