which function has real zeros at x = −10 and x = −6? f(x) = x2 16x 60 f(x) = x2 − 16x 60 f(x) = x2 4x 60 f(x) = x2 − 4x 60

Would assume the function is a quadratic function. It is degree 2.

The zeros or roots are x = - 10, and x = -6.

For quadratic:

x² - (sum of roots)x + product = 0

x² - (-10 + -6)x + (-10)*(-6) = 0

x² - (-16)x + (60) = 0

x² + 16x + 60 = 0

f(x) = x² + 16x + 60

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OrethaWilkison OrethaWilkison · Answer 2 · 2018-11-22T06:50:54-05:00

Answer:

Option A is correct

The function \(x^2+16x+60\) has real zeroes at x =-10 and x =-6

Explanation:

Given: The real zeroes or roots are x = -10, and x = -6

To find the quadratic function of degree 2.

\(x^2- (\alpha+\beta)x + \alpha\beta =0\) where α,β are real roots. ....[1]

Here, α= -10 and β= -6

Sum of the roots:

α+β = -10+(-6) = -10-6 = -16

Product of the roots:

αβ = (-10)(-6)= 60

Substitute these value in equation [1] we have;

\(x^2-(-16)x+60 = x^2+16x+60\)

Therefore, the quadratic function for the real roots at x =-10 and x =-6 ;

\(x^2+16x+60\)