Class 10

Math

All topics

Quadratic Equations

If $sinα=p$, where $∣p∣⩽1$ then quadratic equation whose roots are $tan2α $ and $cot2α $ is

Consider that A quadratic equation $ax_{2}+bx+c=0$ and roots of this equation is $tan2α andcot2α $.

Since we know that if $pandq$ and root of a quadratic equation thenn equation is

$x_{2}−(p+q)x+pq=0$.

So our equation is $x_{2}−(tan2α +cot2α )x+tan2α cot2α =0$

$x_{2}−⎝⎛ cos2α sin2α +sin2α cos2α ⎠⎞ x+1=0$

$x_{2}−⎝⎛ sin2α cos2α sin_{2}2α +cos_{2}2α ⎠⎞ x+1=0$

$x_{2}−⎝⎛ sin2α cos2α 1 ⎠⎞ x+1=0$

$x_{2}−2×sinα1 x+1=0$

$[∵sinα=p]$

$x_{2}−p2 x+1=0$

Which is our required quadratic equation.