Question

what value(s) of 'a' quadratic equation 3ax2 - 6x + 1 = 0 has no real roots?​

Answer 1

Answer :

a > 3

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 ;

3ax² - 6x + 1 = 0

Now ,

Comparing the given quadratic equation with the general quadratic equation Ax² + Bx + C = 0 , we have ;

A = 3a

B = -6

C = 1

Now ,

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

=> D = B² - 4AC

=> D = (-6)² - 4•3a•1

=> D = 36 - 12a

=> D = 12(3 - a)

Also ,

We know that , for no real roots the discriminant of the quadratic equation must be less than zero .

Thus ,

=> D < 0

=> 12(3 - a) < 0

=> 3 - a < 0

=> 3 < a

=> a > 3

Hence , a > 3 .