Determine the zeros of the quadratic function 5x2−11x + 2=0 Solve by factoring or the quadratic formula. Show ALL steps. (2 points)
To find the zeros of the quadratic function 5x^2 - 11x + 2 = 0, we can use either factoring or the quadratic formula.
Method 1: Factoring
To solve by factoring, we need to factorize the quadratic equation 5x^2 - 11x + 2 = 0. It can be factored as (x - 2)(5x - 1) = 0.
Setting each factor equal to zero, we have two equations:
x - 2 = 0 --> x = 2
5x - 1 = 0 --> x = 1/5
The two zeros of the quadratic function are x = 2 and x = 1/5.
Method 2: Quadratic Formula
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 5, b = -11, and c = 2.
Substituting these values into the quadratic formula, we have:
x = (-(-11) ± √((-11)^2 - 4(5)(2))) / (2(5))
= (11 ± √(121 - 40)) / 10
= (11 ± √(81)) / 10
= (11 ± 9) / 10
Therefore, x = (11 + 9) / 10 = 20 / 10 = 2, or x = (11 - 9) / 10 = 2 / 10 = 1/5.
The two zeros of the quadratic function are x = 2 and x = 1/5.
Either method gives the same results.