Modeling and Analyzing Quadratic Functions: Quadratic Equations — Test

Question 4 • Algebra: Concepts and Connections

What are the zeros of the quadratic function f of x is equal to 2 x squared minus 10 x minus 3 ?

Answer

x is equal to negative 5 halves minus the fraction with numerator square root of 31 and denominator 2 and x is equal to negative 5 halves plus the fraction with numerator square root of 31 and denominator 2

x is equal to 5 halves minus square root of 37 eighths and x is equal to 5 halves plus square root of 37 eighths

x is equal to negative 5 halves minus square root of 37 eighths and x is equal to negative 5 halves plus square root of 37 eighths

x is equal to 5 halves minus the fraction with numerator square root of 31 and denominator 2 and x is equal to 5 halves plus the fraction with numerator square root of 31 and denominator 2

Explanation

Set the function equal to zero: 2x² − 10x − 3 = 0. Using the quadratic formula gives x = (10 ± √[(-10)² − 4(2)(−3)]) ÷ 4 = (10 ± √124) ÷ 4. Since √124 = 2√31, the zeros are 5/2 − √31/2 and 5/2 + √31/2, which matches choice D.

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