Which of the following equations has two distinct real roots?
A.

B. x² + x – 5 = 0

C.

D. 5x² - 3x + 1 = 0

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

A. Given,

∴ D = b² - 4ac = 0

= 18 - 18 = 0

Hence, the roots are real and equal.

B. Given, x² + x – 5 = 0

∴ D = b² - 4ac = 0

= (1)² - 4(1) (-5)

= 1 + 20 = 21 > 0

Hence, the roots are real and distinct.

C. Given,

∴ D = b² - 4ac = 0

= 3² - 4(1) (2√2)

Hence, the roots are imaginary.

D. Given, 5x² - 3x + 1 = 0

∴ D = b² - 4ac = 0

= (-3)² - 4(5)(1)

= 9 – 20 < 0

Hence, the roots are imaginary.