SOLUTION: If one root of k(x − 1)2 = 5x−7 is double the other root, show that k = 2 or −25.

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Question 1119477: If one root of k(x − 1)2 = 5x−7 is double the other root, show that k = 2 or −25.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
k%28x-1%29%5E2=5x-7
Algebraic steps lead to
kx%5E2-%282x%2B5%29x%2B%28k%2B7%29=0.


If r is one root, then if as given one root is double the other, other root is 2r.

SUM OF ROOTS
r%2B2r=%282k%2B5%29%2Fk
3r=%282k%2B5%29%2Fk

PRODUCT OF ROOTS
r%2A2r=%28k%2B7%29%2Fk
2r%5E2=%28k%2B7%29%2Fk

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If the sum of roots equation is used to solve for r in terms of k, and then r^2 calculated and substituted into the product-of-roots equation, ... the algebra steps will lead to when simplified, k%5E2%2B23k-50=0.

This factorizes to %28k-2%29%28k%2B25%29=0.