Question

Prove that the roots of (a-b)^2x^2+2(a+b-2c)x+1=0 , a 12 years ago

Answer 1

for the quadratic equation ax^2+bx+c=0 to have imaginary roots, the condition which is to be satisfied is b^2-4ac<0.
use this condition to your equation and then find the condition for c.

Answer 2

\[(a-b)^2x^2+2(a+b-2c)x+1=0\]
\[b^2-4ac \implies \]
\[(2(a+b-2c))^2-4(a-b)^2*1\]

Answer 3

\[4(a^2+b^2+4c^2-2(ab-2ac-2bc)-a^2+2ab-b^2)\]

Answer 4

\[4(4c^2-2ab+4ac+4bc+2ab)\]

Answer 5

\[4(4c^2+4ac+4bc)\]
\[16(c^2+c(a+b))\]

Answer 6

this is real when \[b^2-4ac>0\] real roots
\[c^2+c(a+b) \ge0\]
\[c+a+b \ge 0\]
\[c\ge a+b\]

Answer 7

i mean
\[a+b \ge c\]

Answer 8

for imaginery
\[a+b \le c\]