SOLUTION: Find a quadratic with real coefficients and quadratic term {{{x^2}}} that has {{{5-4i}}} as a root.

Algebra ->  Inequalities -> SOLUTION: Find a quadratic with real coefficients and quadratic term {{{x^2}}} that has {{{5-4i}}} as a root.      Log On


   

Question 1156958: Find a quadratic with real coefficients and quadratic term x%5E2 that has 5-4i as a root.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39615) About Me  (Show Source):
Answer by greenestamps(13198) About Me  (Show Source):
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If the coefficients of the quadratic x%5E2%2Bax%2Bb are real and one root is 5-4i, then the other root is 5%2B4i.

Vieta's Theorem says the sum of the roots is -a and the product is b.

The sum of the roots is 10; so -a=10 which means a = -10.

The product of the roots is 25-16i%5E2+=+25%2B16+=+41; so b = 41.

ANSWER: x%5E2-10x%2B41