Find a polynomial with zeros at x=5, x=-3, and x=1, that also contains the point (2,3).

Suman Cole

Suman Cole

Answered question

2020-12-25

Find a polynomial with zeros at x=5, x=-3, and x=1, that also contains the point (2,3).

Answer & Explanation

Luvottoq

Luvottoq

Skilled2020-12-26Added 95 answers

Given the zeros 5, —3, and 1, we can write the polynomial as: y= a(x —5)(x+3)(x—1)
To find a, we substitute (x,y) = (2,3) since the polynomial contains it:
3=a(2—5)(2+3)(2—1)
3 = a(—3)(5)(1)
3 = -15a
(15)=a
So, the polynomial function is:
y=(15)(x5)(x+5)(x1)
or when expanded,
y=(15)(x22x15)(x1)
y=(15)[x2(x1)2x(x1)15(x1)]
y=(15)(x3x22x2+2x15x+15)
y=(15)(x33x213x+15)
y=(15)x3+35x2+135x3
Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-10Added 2605 answers

Answer is given below (on video)

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