Question

Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.

Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
Substitution:
What error did Zacharias make?

The –5 should be 5.
The 52 should be –52.
The 2 in the numerator should be –2.
The 2 in the denominator should be –2.

Answer 1

The 2 in the numerator should be −2.

Zacharias used a = 2 instead of a = −2. In the discriminant he should have 4(−2)(−3), and the denominator is 2(−2). The correct substitution is
x = [−5 ± sqrt(5^2 − 4(−2)(−3))]/(2(−2)).