Solve the quadratic equation 6x2−3x+6=0 . Which of the following expresses its solutions in the form a±bi
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GPT-5 mini
AI
Use the quadratic formula:
x = [3 ± sqrt((-3)^2 − 4·6·6)]/(2·6) = [3 ± sqrt(9 − 144)]/12 = [3 ± sqrt(−135)]/12
= [3 ± 3i√15]/12 = 1/4 ± (i√15)/4.
So the solutions are x = 1/4 ± (i√15)/4 (or (1 ± i√15)/4).
x = [3 ± sqrt((-3)^2 − 4·6·6)]/(2·6) = [3 ± sqrt(9 − 144)]/12 = [3 ± sqrt(−135)]/12
= [3 ± 3i√15]/12 = 1/4 ± (i√15)/4.
So the solutions are x = 1/4 ± (i√15)/4 (or (1 ± i√15)/4).
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