Question

Is equation x^2 + 2 root3x - 1 = 0 has real root or
not?​

Answer 1

Answer :

Real 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

★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

★ If α and ß are the roots of a quadratic equation , then that quadratic equation is given as : k•[ x² - (α + ß)x + αß ] = 0 , k ≠ 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 ;

x² + 2√3x - 1 = 0

Now ,

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

a = 1

b = 2√3

c = -1

Now ,

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

=> D = b² - 4ac

=> D = (2√3)² - 4•1•(-1)

=> D = 4•3 - 4

=> D = 12 - 4

=> D = 8

=> D > 0

Clearly ,

The discriminant D > 0 , thus the given quadratic equation has real and distinct roots .

Hence ,

The given equation has real roots .