Q. 94.1( 11 Votes )

# Which of the following equations has two distinct real roots?

A.

B. x^{2} + x – 5 = 0

C.

D. 5x^{2} - 3x + 1 = 0

Answer :

Same as the previous one. Let’s check the discriminant value for distinct real roots.

A. Given,

**∴** D = b^{2} - 4ac = 0

= 18 - 18 = 0

Hence, the roots are real and equal.

B. Given, x^{2} + x – 5 = 0

**∴** D = b^{2} - 4ac = 0

**=** (1)^{2} - 4(1) (-5)

= 1 + 20 = 21 > 0

Hence, the roots are real and distinct.

C. Given,

**∴** D = b^{2} - 4ac = 0

= 3^{2} - 4(1) (2√2)

Hence, the roots are imaginary.

D. Given, 5x^{2} - 3x + 1 = 0

**∴** D = b^{2} - 4ac = 0

= (-3)^{2} - 4(5)(1)

= 9 – 20 < 0

Hence, the roots are imaginary.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Bonus Questions on Solutions of Quadratic Equations31 mins

Get To Know About Quadratic Formula42 mins

Smart Revision | Quadratic Equations53 mins

Quiz | Knowing the Nature of Roots44 mins

Take a Dip Into Quadratic graphs32 mins

Foundation | Practice Important Questions for Foundation54 mins

Learn to Find Nature of Roots25 mins

Nature of Roots of Quadratic Equations51 mins

Getting Familiar with Nature of Roots of Quadratic Equations51 mins

Understand The Concept of Quadratic Equation45 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation