Question

what will be the nature of the roots of the quadratic equation 5x²- 4x + 5= 0​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ 5x² - 4x + 5 = 0.

As we know that,

⇒ D = Discriminant  Or b² - 4ac.

⇒ D = (-4)² - 4(5)(5).

⇒ D = 16 - 100.

⇒ D = -84.

⇒ D < 0 Roots are imaginary.

                                                                                                                       

MORE INFORMATION.

Nature of the roots 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

No root exists!

Step-by-step explanation:

Solution:

According to the question, A quadratic equation is given: 5x² - 4x + 5 = 0. We need to find the nature of its roots.

Discriminant of a quadratic equation determines the nature of roots. It tells whether the roots are distinct, equal or unreal. It is determined by the formula b² - 4ac.

• b² - 4ac > 0 [Real and distinct]
• b² - 4ac = 0 [Real and equal]
• b² - 4ac < 0 [Unreal]

From the given quadratic equation, we can observe that:

• a = 5
• b = -4
• c = 5

On finding discriminant, we get:

D = b² - 4ac

D = (-4)² - (4 × 5 × 5)

D = 16 - 100

D = -84

We can observe that, D(-84) < 0, which means the roots are unreal. Therefore, no roots exist!

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