The quadratic equation 2x2 – √5x + 1 = 0 has(a) two distinct real

1.	The quadratic equation 2x2 – √5x + 1 = 0 has(a) two distinct real roots(b) two equal real roots(c) no real roots(d) more than 2 real roots
Answer» (c) no real roots The discriminant value of a quadratic equation ax² + bx + c = 0, a ≠ 0 is given by, D = b² - 4ac = 0 i. If D = b² - 4ac > 0, then its roots are distinct and real. ii. If D = b² - 4ac = 0, then its roots are real and equal. iii. If D = b² - 4ac < 0, then its roots are imaginary. Given, 2x² – √5x + 1 = 0 ∴ D = b² - 4ac = 0 = (-√5)² - 4(2)(1) = -3 < 0 Hence, the roots of the quadratic equation 2x² – √5x + 1 = 0 are imaginary.

The quadratic equation 2x2 – √5x + 1 = 0 has(a) two distinct real roots(b) two equal real roots(c) no real roots(d) more than 2 real roots

Answer»

(c) no real roots

The discriminant value of a quadratic equation ax² + bx + c = 0, a ≠ 0 is given by,

D = b² - 4ac = 0

i. If D = b² - 4ac > 0, then its roots are distinct and real.

ii. If D = b² - 4ac = 0, then its roots are real and equal.

iii. If D = b² - 4ac < 0, then its roots are imaginary.

Given, 2x² – √5x + 1 = 0

∴ D = b² - 4ac = 0

= (-√5)² - 4(2)(1)

= -3 < 0

Hence, the roots of the quadratic equation 2x² – √5x + 1 = 0 are imaginary.