How do you find the quadratic equation that has the following roots: #4+-3isqrt2#?
1 Answer
Sep 12, 2017
Explanation:
We are given that the quadratic sought has roots
# 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 #
