Instructions: Solve each equation using the Quadratic Formula. Enter your answers from least to greatest.2x2−8x−10=0
Question
Solve each equation using the Quadratic Formula. Enter your answers from least to greatest.
Solution
The quadratic formula is given by:
x = [-b ± sqrt(b² - 4ac)] / 2a
For the equation 2x² - 8x - 10 = 0, the coefficients are a = 2, b = -8, and c = -10.
Step 1: Calculate the discriminant (b² - 4ac)
Discriminant = (-8)² - 42(-10) = 64 + 80 = 144
Step 2: Substitute a, b, and the discriminant into the quadratic formula
x = [8 ± sqrt(144)] / 4 = [8 ± 12] / 4
So the solutions are x = 20/4 = 5 and x = -4/4 = -1.
Therefore, the solutions from least to greatest are -1 and 5.
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