Question

Find the exact zeros of the function
f(x) = 25x^2 − 10x − 1

Answer 1

x = 1/5 + √(2)/5 = 0.483

or

x = 1/5 - √(2)/5 = -0.083

Explanation:

When a math problem asks to find the "zeroes" of the equation, it is asking for the x-intercepts of the equation. In other words, you must set the equation equal to zero.

Solve for x over the real numbers:

25 x^2 - 10 x - 1 = 0

Write the quadratic equation in standard form.

Divide both sides by 25:

x^2 - 2x/5 - 1/25 = 0

Solve the quadratic equation by completing the square.

Add 1/25 to both sides:

Take one half of the coefficient of x and square it, then add it to both sides.

x^2 - 2x/5 + 1/25 = 1/25 + 1/25

Factor the left hand side.

Write the left hand side as a square:

(x - 1/5)^2 = 2/25

Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 1/5 = (√2)/5 or x - 1/5 = (-√2)/5

Look at the first equation: Solve for x.

Add 1/5 to both sides:

x = 1/5 + √(2)/5 or x = 1/5 - √(2)/5

Answer 2

answer attached

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.