Question

Find the nature of roots of the quadratic equations 9x2-6x-2=0.

Answer 1

Concept Used :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

• If Discriminant, D > 0, then roots of the equation are real and unequal.

• If Discriminant, D = 0, then roots of the equation are real and equal.

• If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

• Discriminant, D = b² - 4ac

Let's solve the problem now!!!!

$\green{\large\underline{\bf{Solution-}}}$

Given quadratic equation is

$\rm :\longmapsto\: {9x}^{2} - 6x - 2 = 0$

$\rm :\longmapsto\:On \: comparing \: with \: {ax}^{2} + bx + c = 0$

we have,

$\red{\bf :\longmapsto\:a = 9 \: \: \: } \\ \red{\bf :\longmapsto\:b = - 6} \\ \red{\bf :\longmapsto\:c = - 2}$

Now, Discriminant, D is given by

$\green{\bf :\longmapsto\:Discriminant,D = {b}^{2} - 4ac}$

$\rm :\longmapsto\:D = {( - 6)}^{2} - 4 \times (9) \times ( - 2)$

$\rm :\longmapsto\:D = 36 + 72$

$\rm :\longmapsto\:D = 108$

$\bf\implies \:D > 0$

Hence,

$\underbrace{\boxed{ \bf{9x}^{2} - 6x - 2 = 0 \: has \: real \: and \:unequal\: roots.}}$