Question

find the discrimination of t he equation 2x raise to 5 -5x +3=0 and hence write the nature of the roots​

Answer 1

Answer :

• Discriminant , D = 1

• Nature of roots : Real and distinct

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 - 5x + 3 = 0

Now ,

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

a = 2

b = -5

c = 3

Now ,

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

=> D = b² - 4ac

=> D = (-5)² - 4•2•3

=> D = 25 - 24

=> D = 1

=> D > 0

Clearly ,

The discriminant of the given quadratic equation is greater than zero .

Hence ,

It has real and distinct roots .