Asked by tt
Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x2-x=-4
has.
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the equation as 2x^2 − x = −4. Move all terms to one side:
2x^2 − x + 4 = 0.
Compute the discriminant D = b^2 − 4ac with a = 2, b = −1, c = 4:
D = (−1)^2 − 4(2)(4) = 1 − 32 = −31.
Because D < 0 there are no real solutions; there are two complex conjugate solutions:
x = [−b ± sqrt(D)]/(2a) = (1 ± i√31)/4.
2x^2 − x + 4 = 0.
Compute the discriminant D = b^2 − 4ac with a = 2, b = −1, c = 4:
D = (−1)^2 − 4(2)(4) = 1 − 32 = −31.
Because D < 0 there are no real solutions; there are two complex conjugate solutions:
x = [−b ± sqrt(D)]/(2a) = (1 ± i√31)/4.
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