Question

find the value of discriminate for the quadratic equation x2+2x_9=0​

Answer 1

EXPLANATION.

Discriminant of the quadratic equation.

⇒ x² + 2x - 9 = 0.

As we know that,

D = Discriminant

⇒ D = b² - 4ac.

⇒ D = (2)² - 4(1)(-9).

⇒ D = 4 + 36.

⇒ D = 40.

                                                                                                                     

MORE INFORMATION.

Nature of the factor of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Real and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

$\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{a \: quadratic \: equation} \\ &\sf{ {x}^{2} + 2x - 9 = 0 } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To\:find - \begin{cases} &\sf{nature \: of \: roots}  \end{cases}\end{gathered}\end{gathered}$

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

$\large\underline{\bold{Solution :- }}$

The given

• Quadratic equation is x² + 2x - 9 = 0

On comparing, with ax² + bx + c = 0, we get

• a = 1

• b = 2

• c = - 9

Now,

• Discriminant, D is given by

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

$\rm :\longmapsto\:D = {2}^{2} - 4 \times 1 \times ( - 9)$

$\rm :\longmapsto\:D = 4 + 36$

$\rm :\longmapsto\:D = 40$

$\rm :\implies\: \boxed{ \bf \: D > 0}$

So,

• Equation x² + 2x - 9 = 0 has real and unequal roots.