Question

. If a, B are the roots of equation x²- 5x+6=0 and a. > B then the equation with roots (aß+a+ß)
and (aß-a-ß) is
(a) x²-12x+11=0 (b) 2x²- 6x+12=0 (C) x²-12x+12=0 (d) None​

Answer 1

$\alpha \: and \: \beta$ are the roots of the equation x² - 5x + 6 = 0

=> $\alpha + \beta = \frac{-b}{a} = 5$

=> $\alpha \beta = \frac{c}{a} = 6$

now,

$\alpha \beta + \alpha + \beta = 6 + 5 = 11$

$\alpha \beta - \alpha - \beta = 6 - 5 = 1$

now, let

$\gamma = 11 \: and \: \delta = 1$

now, equation with $\gamma$ and $\delta$ as its roots is

x² - (11 + 1)x + (11)(1) = 0

x² - 12x + 11 = 0