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