62.4k views
0 votes
Write a quartic polynomial function in standard formgiven zeros at:x= -3,0,3,4

User Mushi
by
3.3k points

1 Answer

4 votes

Take into account that for a polynomial with zero x=a, one of its factors is (x - a), then, for zeros z=-3,0,3,4, you have

f(x) = (x - (-3))(x - 0)(x - 3)(x - 4)

expand the previous factors:

f(x) = (x + 3)(x)(x - 3)(x - 4)

= x(x + 3)(x - 3)(x - 4) multiply first two factors and last two factors

= (x² + 3x)(x² - 4x - 3x + 12)

= (x² + 3x)(x² - 7x + 12)

= x⁴ - 7x³ + 12x² + 3x³ - 21x² + 36x

= x⁴ - 4x³ - 9x² + 36x

Hence, the quartic polynomial is x⁴ - 4x³ - 9x² + 36x

User Reidark
by
3.1k points