Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. he begins by substituting as shown. quadratic formula: x = startfraction negative b plus or minus startroot b squared minus 4 a c endroot over 2 a endfraction substitution: x = startfraction negative 5 plus or minus startroot 5 squared minus 4(2)(negative 3) endroot over 2(negative 2) endfraction what error did zacharias make? the –5 should be 5. the 52 should be –52. the 2 in the numerator should be –2. the 2 in the denominator should be –2

The 2 in the numerator should be –2

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

The 2 in the numerator should be –2

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.