Question

Find a polynomial function with the zeros -3(multiplicity 2) and 3(multiplicity), whose graph passes through the point (-4, 147).

Answer 1

Given :  a polynomial function with the zeros -3(multiplicity 2) and 3(multiplicity 2), whose graph passes through the point (-4, 147).

To Find :  polynomial function

Solution:

a polynomial function with the zeros -3(multiplicity 2) and 3(multiplicity 2)

P(x)= a(x - (-3))²(x - 3)²

= a (x + 3)²(x - 3)²

x = -4 , P(x) = 147

=>  a(-4 + 3)²(-4 - 3)² = 147

=> a (-1)²(-7)² = 147

=> a (1)(49) = 147

=> a = 3

P(x)= 3(x + 3)²(x - 3)²

=> P(x) = 3(x² - 9)²

=> P(x) = 3 (x⁴ -18x² + 81)

=> P(x) = 3x⁴ - 54x² + 243

P(x) = 3x⁴ - 54x² + 273

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