Question

The roots of the equation x2-3x-9 = 0 are:
a)real and unequal b) real and equal c)roots are not equal d)imaginary roots

Answer it !

Answer 1

Real and unequal
Discriminant= 9+36=45>0
So the roots are real and unequal

Answer 2

QuestioN :

The roots of the equation x2-3x-9 = 0 are:

a)real and unequal

b) real and equal

c)roots are not equal

d)imaginary roots

GiveN :

x² - 3x - 9 = 0

To FiNd :

• The nature of the roots of the equation.

ANswer :

a)real and unequal

SolutioN :

We know,

A quadratic equation us always in the form:-

ax² + bx + c.

The discriminant of the quadratic equation is:-

• b² - 4ac

We have,

Equation = x² - 3x - 9

Here the given equation us in the form ax² + bx + c

Hence,

On comparing we get,

• a = 1 (Coefficient of x²)
• b = -3 (Coefficient of x)
• c = -9 (Constant Term)

Putting the values in the discriminant of a quadratic equation:-

= b² - 4ac

= (-3)² - 4 × (1) × (-9)

= 9 + 36

= 45

Here, b² - 4ac > 0

∴Hence,  The given equation will have two distinct real roots.

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