Question

if the equations 2x^2+bx+8=0 has equal roots , find the value of b​

Answer 1

Answer :

b = ± 8

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 + bx + 8 = 0

Now ,

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

a = 2

b = b

c = 8

We know that ,

For equal roots , the discriminant of the quadratic equation must be zero .

Thus ,

=> D = 0

=> b² - 4ac = 0

=> b² - 4•2•8 = 0

=> b² - 64 = 0

=> b² = 64

=> b = √64

=> b = ± 8

Hence , b = ± 8 .