Which statement best describes the zeros of the function h(x) = (x − 4)2(x2 − 7x + 10)? A.
The function has four complex zeros.
B.
The function has three distinct real zeros.
C.
The function has two distinct real zeros and two complex zeros.
D.
The function has four distinct real zeros.
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i can

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4