Question

5. Given (x + 1) and (x-3) are factors of P(x) = x4-5x³-7x² + cx + d. Determine the values

Answer 1

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

How to determine the missing coefficients of a quartic equation

A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of linear equations:

(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0    

- c + d = 1      (1)

3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0    

3 · c + d = 117       (2)

The solution of this system is c = 29 and d = 30.

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

To learn more on polynomials: brainly.com/question/11536910

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