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Sagot :
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
What are the x-intercepts of a quadratic equation?
A quadratic equation is modeled by:
y = ax² + bx + c.
The x-intercepts are the values of x when y = 0, given by:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the equation is:
y = 60 + 28x - x².
Hence the coefficients are a = -1, b = 28, c = 60.
Then:
[tex]\Delta = 28^2 - 4(-1)(60) = 1024[/tex]
[tex]x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2[/tex]
[tex]x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30[/tex]
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
More can be learned about quadratic equations at https://brainly.com/question/24737967
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