Question

the nature of the roots for the quadratic equation X square - x minus 20 is equal to zero​

Answer 1

$\huge\ \: { \underline{ \boxed{ \pink{ \pmb{ \frak{ \: Answeꋪ \: }}}}}}$

Find the nature of the roots of the given quadratic equation by using discriminant condition.

$\longmapsto \: {x2−x−2=0}$

The give equation is in the form of,

${a}^{2} + bx + c = 0$

So,

$\implies \: a = 1$

$\implies \: b = - 1$

$\implies \: c = - 2$

Finding the discriminant of the equation,

$\implies \: D = {b}^{2} - 4ac$

putting the values of a, b and c,

$\longmapsto \: D = {( - 1)}^{2} - 4(1) ( - 2)$

$\implies \: D = 9$

$\implies \: D > 0$

Since, D is positive, so, the equation has two distinct real roots.

Hence, the roots of the quadratic equation

$\green{ \sf{ {x}^{2} - x - 2 = 0 \: are \: real \: in \: nature}}$

$\purple{ \pmb{ \frak{hope \: its \: help \: u}}}$