Find the exact solutions to the quadratic equation below, using the quadratic formula. Enter the smaller number first.−3x2−5x+2=0
Question
Solution
The quadratic formula is given by:
x = [-b ± sqrt(b² - 4ac)] / 2a
In the equation -3x² - 5x + 2 = 0, the coefficients are a = -3, b = -5, and c = 2.
First, calculate the discriminant, which is b² - 4ac:
Discriminant = (-5)² - 4*(-3)*2 = 25 + 24 = 49
Since the discriminant is positive, there are two distinct real roots.
Now, substitute a, b, and the discriminant into the quadratic formula to find the solutions:
x = [5 ± sqrt(49)] / 2*(-3) x = [5 ± 7] / -6
So the solutions are x = -2/3 and x = -4.
The smaller number is -4.
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