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 1

Given Equation:-

• x² - 3x - 9 = 0

To find:-

• The nature of the roots of the equation.

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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Extra Informations:-

The quadratic equation is in the form ax² + bx + c whose discriminant is b² - 4ac.

A quadratic equation, has:-

• two distinct real roots, if b² - 4ac > 0
• two equal real roots, if b² - 4ac = 0
• no real roots, if b² - 4ac < 0

Discriminant:- b² - 4ac is called the discriminant of a quadratic equation as it determines the nature of the roots of a quadratic equation.

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