Solving Quadratic Equations: Quadratic Formula — Quiz
Question 9 • Algebra: Concepts and Connections
In simplest radical form, what are the solutions to the quadratic equation 0 is equal to negative 3 x squared minus 4 x plus 5 ? Quadratic formula: x is equal to the fraction with numerator negative b plus or minus square root of b squared minus 4 A c end root and denominator 2 A
Answer
A
x is equal to negative the fraction with numerator 2 plus or minus 2 square root of 19 and denominator 3
B
x is equal to negative the fraction with numerator 2 plus or minus square root of 19 and denominator 3
C
x is equal to the fraction with numerator 2 plus or minus square root of 19 and denominator 3
D
x is equal to the fraction with numerator 2 plus or minus 2 square root of 19 and denominator 3
Explanation
For −3x² − 4x + 5 = 0, the coefficients are a = −3, b = −4, and c = 5. The discriminant is b² − 4ac = 16 − 4(−3)(5) = 76, so its square root is 2√19. Substituting into the quadratic formula gives x = (4 ± 2√19)/(−6) = −(2 ± √19)/3. This matches choice B: x = −(2 ± √19)/3.
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