Question

the number of equations of the form a x square + bx + 2 equal to zero that can be formed if the equation have real roots is /are

Answer 1

Heya

Calculating the discriminant of the equation :
${b}^{2} - 8a \geqslant 0$

$= > {b}^{2} \geqslant 8a$

But,
$a \geqslant 2$

$= > 36 \geqslant {b}^{2} \geqslant 16$
$\\ = > 4 \leqslant b \leqslant 6$
And hence, we have the following pairs :

( a , b ) = { ( 2 , 4 ) , ( 2 , 5 ) , ( 3 , 5 ) , ( 2 , 6 ) , ... , ( 4 , 6 ) }

And hence, there are 6 such possible equations..