The Quadratic Formula — Quiz

Question 9 • Advanced Algebra: Concepts and Connections

Which equation shows the quadratic formula used correctly to solve 5 x squared plus 3 x minus 4 is equal to 0 for x ?

Answer

x is equal to the fraction with numerator 3 plus or minus square root of 3 squared plus 4 5 negative 4 end root and denominator 2 times 5

x is equal to the fraction with numerator 3 plus or minus square root of 3 squared minus 4 5 negative 4 end root and denominator 2 times 5

x is equal to the fraction with numerator negative 3 plus or minus square root of 3 squared minus 4 5 negative 4 end root and denominator 2 times 5

x is equal to the fraction with numerator negative 3 plus or minus square root of 3 squared plus 4 5 negative 4 end root and denominator 2 times 5

Explanation

For 5x² + 3x − 4 = 0, the coefficients are a = 5, b = 3, and c = −4. The quadratic formula is x = (−b ± √(b² − 4ac))/(2a), so substituting gives x = (−3 ± √(3² − 4·5·(−4)))/(2·5). This matches choice D.

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