Question
Find a polynomial function of least degree with real coefficients satisfying the given properties.
zeros -3, 0, and 4
f(1) =10
zeros -3, 0, and 4
f(1) =10
Answers
if zeros are -3, 0, 4, it could be
f(x) = x(x+3)(x-4)
but (1,10) lies on it , so we have to stretch it to pass through that point without wrecking the zeros
f(x) = ax(x+3)(x-4)
10 = a(4)(-3)
-12a = 10
a = -5/6
f(x) = -(5/6)x(x+3)(x-4)
f(x) = x(x+3)(x-4)
but (1,10) lies on it , so we have to stretch it to pass through that point without wrecking the zeros
f(x) = ax(x+3)(x-4)
10 = a(4)(-3)
-12a = 10
a = -5/6
f(x) = -(5/6)x(x+3)(x-4)
Thank you.
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