Question

for what values of m will the equation have real and distinct roots​

Answer 1

Answer:

$m \geqslant \frac{ - 1}{2}$

Step-by-step explanation:

The equation has real and distinct roots

So

$b {}^{2} - 4ac \geqslant 0$

$= > (2(1 + 2m)) {}^{2} - 4 \times 2m(1 + 2m) \geqslant 0$

$= > 4(1 + 2m) {}^{2} - 8m(1 + 2m) \geqslant 0$

$= > 4(1 + 2m \geqslant 0$

$= > 1 + 2m \geqslant 0$

$so \: \: m \geqslant \frac{ - 1}{2}$

$so \: for \: m \geqslant \frac{ - 1}{2} \: equation \: has \: real \: and \: distinct \: roots$

$= > 4(1 + 2m)(1 + 2m - 2m) \geqslant 0$