Question

Find the nature of the roots:
2x2 -3x+5=0

Answer 1

Given ,

The quadratic equation is 2x² - 3x + 5 = 0

Thus , the discriminant of given quadratic equation is

D = (-3)² - 4 × 2 × 5

D = 9 - 40

D = -31 < 0

Therefore , the given equation has no real roots or imaginary roots

Answer 2

Answer : The roots of the 2x² - 3x + 5 are unreal and imaginary Step-by-step Explanation : Given : Quadratic Equation : 2x² - 3x + 5 = 0 To find : Nature of the roots = ? We know that, Nature of the roots depends on b²- 4ac If, b² - 4ac > 0 : Roots are real and distinct b² - 4ac = 0 : Roots are real and same b² - 4ac < 0 : Roots are Imaginary In the given equation we have, a = 2 , b = -3 and c = 5 So substituting in b² - 4ac we get, b² - 4ac = (-3)² - 4(2)(5) = 9 - 40 = -31 or < 0 Since b² - 4ac = -31 which is les than Zero Hence the roots of the 2x² - 3x + 5 are unreal and imaginary