Question

The function, f(x) = –2x2 + x + 5, is in standard form. The quadratic equation is 0 = –2x2 + x + 5, where a = –2, b = 1, and c = 5. The discriminate b2 – 4ac is 41. Now, complete step 5 to solve for the zeros of the quadratic function.



5. Solve using the quadratic formula.

x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction



What are the zeros of the function
f(x) = x + 5 – 2x2?

x = StartFraction negative 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction
x = StartFraction 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction
x = StartFraction negative 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction
x = StartFraction 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction

Answer 1

Use a = -2, b = 1, c = 5.
x = [-b ± sqrt(b^2 - 4ac)]/(2a) = [-1 ± sqrt(41)]/(-4).

Simplifying gives the zeros x = (1 ± sqrt(41))/4, i.e. x = (1 + sqrt(41))/4 and x = (1 - sqrt(41))/4.

(Choice 1 is correct.)