Question

Determine k so that the equation x2- 4x +k = 0 has
(ii) coincident roots

Answer 1

Answer :

k = 4

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 ;

x² - 4x + k = 0

Now ,

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

a = 1

b = -4

c = k

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

Thus ,

=> D = 0

=> b² - 4ac = 0

=> (-4)² - 4•1•k = 0

=> 16 - 4k = 0

=> 4k = 16

=> k = 16/4

=> k = 4

Hence , k = 4 .