Question

Write the nature of roots 2x^-3x+5=0

Answer 1

Answer :

Imaginary roots

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; ax² + bx + c = 0

★ The discriminant , D of the quadratic equation ax² + bx + c = 0 is given by ;

D = b² - 4ac

★ If D = 0 , then the roots are real and equal .

★ If D > 0 , then the roots are real and distinct .

★ If D < 0 , then the roots are unreal (imaginary) .

Solution :

Here ,

The given quadratic equation is ;

2x² - 3x + 5 = 0

Now ,

Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 , we have ;

a = 2

b = -3

c = 5

Now ,

The discriminant of the given quadratic equation will be given as ;

=> D = b² - 4ac

=> D = (-3)² - 4•2•5

=> D = 9 - 40

=> D = -31

=> D < 0

Since the discriminant of the given quadratic equation is less than zero , hence it will have imaginary roots .