How do you find the quadratic equation that has the following roots: #4+-3isqrt2#?

1 Answer
Sep 12, 2017

Answer:

#x^2 -8x + 34 = 0#

Explanation:

We are given that the quadratic sought has roots #4+-3isqrt(2)#, denote the roots by:

# alpha = 4-3isqrt(2) #
# beta = 4+3isqrt(2) #

So, given these roots, we have:

# alpha + beta = 4-3isqrt(2) + 4+3isqrt(2) #
# " " = 8 #

# alpha \ beta = (4-3isqrt(2))(4+3isqrt(2)) #
# " " = (4)^2 - (3isqrt(2))^2 #
# " " = 16 + 9*2 #
# " " = 16 + 18 #
# " " = 34 #

And so the equation we seek ijus:

# x^2 -(alpha + beta)x + alpha beta = 0 #
# :. x^2 -8x + 34 = 0 #