Solve for f.f2–5f=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
Question
Solve for f.f2–5f=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
Solution
The given equation is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -5, and c = 0.
Step 1: Identify the coefficients a, b, and c in the equation. Here, a = 1, b = -5, and c = 0.
Step 2: Use the quadratic formula to solve for f. The quadratic formula is given by:
f = [-b ± sqrt(b^2 - 4ac)] / (2a)
Step 3: Substitute the values of a, b, and c into the quadratic formula:
f = [5 ± sqrt((-5)^2 - 410)] / (2*1) f = [5 ± sqrt(25)] / 2 f = [5 ± 5] / 2
Step 4: Solve for f:
f = (5 + 5) / 2 = 10 / 2 = 5 f = (5 - 5) / 2 = 0 / 2 = 0
So, the solutions to the equation f^2 - 5f = 0 are f = 0 and f = 5.
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