Question

If one root of k(x - 1)2 = 5x – 7 is double the other root,show that ​

Answer 1

Answer:

Step-by-step explanation: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

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.