someone please help me slove this problem.
Use the qudratic formula to find any x-intercepton the graph of the equation.
y=4x^2-2x-5
solve 4x^2 - 2x - 5 = 0
x = (2 ± √84)/8
= (2 ± 2√21)/8
= (1 ± √21)/4 ---> the 2 x-intercepts (notice the correct spelling)
To find the x-intercepts of the graph represented by the given equation, you can use the quadratic formula. The quadratic formula is used to solve quadratic equations of the form ax^2 + bx + c = 0.
In this case, the equation is y = 4x^2 - 2x - 5.
Step 1: Write down the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Step 2: Identify the values of a, b, and c in the equation.
In our equation, a = 4, b = -2, and c = -5.
Step 3: Substitute the values of a, b, and c into the quadratic formula.
x = (-(-2) ± √((-2)^2 - 4 * 4 * -5)) / (2 * 4)
Simplifying further,
x = (2 ± √(4 + 80)) / 8
x = (2 ± √84) / 8
x = (2 ± 2√21) / 8
Step 4: Simplify the expression further if possible.
x = (1 ± √21) / 4
So, the x-intercepts of the graph represented by the equation y = 4x^2 - 2x - 5 are:
x = (1 + √21) / 4
x = (1 - √21) / 4
These are the two solutions for x-intercepts of the graph.