Question

Find the nature of roots of the quadratic equation 2x2 - 3x - 4 = 0
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Answer 1

EXPLANATION.

Quadratic equation.

⇒ 2x² - 3x - 4 = 0.

As we know that,

D = Discriminant  Or  b² - 4ac.

⇒ D = (-3)² - 4(2)(-4).

⇒ D = 9 + 32.

⇒ D = 41.

nature of roots is,

⇒ D > 0 Roots are real and unequal.

                                                                                                                           

MORE INFORMATION.

Nature of the factors of the quadratic expression.

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

(2) = Rational 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

Answer:

• The roots are real and distinct.

Step-by-step explanation:

Given

• 2x² - 3x - 4 = 0

To find

• Nature of roots

Solution

General form of the quadratic equation:

• ax² + bx + c = 0

Where:

• a = 2
• b = -3
• c = -4

The discriminant of the given quadratic equation:

• D = b² - 4ac

Substituting we get:

• D = (-3)²-4(2)(-4)
• D = 9 - 4(-8)
• D = 9 + 32
• D = 41

The discriminant of the given quadratic equation is greater than zero.

Hence, the roots are real and distinct.