Question

Solve for the zeros of the quadratic function f(x) = x + 5 – 2x2.

1. Put the quadratic function in standard form.
f(x) = –2x2 + x + 5

2. Set the function equal to 0 to create a quadratic equation.
–2x2 + x + 5 = 0

3. Determine the values for a, b, and c.
a =

b =

c =

4. Analyze the discriminant.
b2 – 4ac =

The quadratic function will have
.

Answer 1

1. Standard form: f(x) = −2x^2 + x + 5

2. Set to zero: −2x^2 + x + 5 = 0

3. a = −2
b = 1
c = 5

4. Discriminant: b^2 − 4ac = 1 − 4(−2)(5) = 1 + 40 = 41

The quadratic will have two distinct real (irrational) zeros.

Zeros: x = (1 ± √41) / 4 (approximately x ≈ −1.3508 and x ≈ 1.8508).