Can someone show me how to do these?

Question

Find a polynomial Q has a degree 3 and zeros 4, 3i,-3i

P has a degree 3 .zeros 5,i and -i Thanks!?

 

Answer 1

The polynomial Q is cubic polynomial.

And the zeros are 4, 3i and -3i.

Q(x) = (x - 4)(x - 3i)(x + 3i)

= (x - 4)[x² - (3i)²]

= (x - 4)[x² - 9(-1)]

= (x - 4)(x² + 9)

= x(x²) + x(9) - 4(x²) - 4(9)

= x³ + 9x - 4x² - 36

Q(x) = x³ - 4x² + 9x - 36.

Answer 2

P is a cubic polynomial.

Zeros of P are 5, i and - i

P(x) = (x - 5)(x - i)(x + i)

= (x - 5)[x² - (i)²]

= (x - 5)[x² - (- 1)]

= (x - 5)(x² + 1)

= x(x²)+ x(1) - 5(x²) - 5(1)

= x³ + x - 5x² - 5

P(x) = x³ - 5x² + x - 5.