SOLUTION: Write the quadratic equation with a lead coefficient of 1 whose roots are 1+3i and 1-3i. Could someone show me how to this step-by-step, please?

Question 67418This question is from textbook Advanced mathematics
: Write the quadratic equation with a lead coefficient of 1 whose roots are 1+3i and 1-3i.
Could someone show me how to this step-by-step, please? This question is from textbook Advanced mathematics

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Say you have these for roots: (x - 5)(x + 1) or x^2 - 4x - 5
Your roots would be 5 and -1 because you would take the opposite (negative value) of the value in the parenthesis.
(x - (1 + 3i))(x - (1 - 3i))
(x - 1 - 3i)(x - 1 + 3i)
x^2 - x - 3xi - x + 1 + 3i + 3xi - 3i + 9
x^2 - 2x + 10
Check:
x^2 - 2x = -10
(x - 1)^2 = -9
x - 1 = +- 3i
x = 1 +- 3i
RELATED QUESTIONS
Write the quadratic equation with a lead coefficient of 1 whose roots are 2-3i and... (answered by Nate)

write the quadratic equation with a lead coefficient of 1 whose roots are 3 and... (answered by robertb)

Write the quadratic equation with a lead coefficient of 1 whose roots are -1/2 and... (answered by stanbon)

Write the quadratic equation with a lead coefficient of 1 whose roots are (-1/2)... (answered by checkley71)

Write the quadratic equation with a lead coefficient of 1 whose roots are 3 and... (answered by stanbon)

Write the quadratic equation with a lead coefficient of 1 whose roots are -2 and 7... (answered by josgarithmetic)

Write the quadratic equation with a lead coefficient of 1 whose roots are 1+ square root... (answered by josmiceli)

Write the quadratic equation with a lead coefficient of 1 whose roots are 1+4i and 1-4i.... (answered by ikleyn)

Write the quadratic equation with a lead coefficient of 1 whose roots are 2+ square root... (answered by Nate)