Q. for
which values of p quadratic
quation 3xsquare -5x +p=0 has equal roots
Answers
Answer:
b^2-4ac = 0
5^2 -4*3*p =0
25-12p =0
12p =25
p = 25/12
Answer :
p = 25/12
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 ;
3x² - 5x + p = 0
Now ,
Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 , we have ;
a = 3
b = -5
c = p
Now ,
The discriminant of the given quadratic equation will be given as ;
=> D = b² - 4ac
=> D = (-5)² - 4•3•p
=> D = 25 - 12p
Also ,
It is given that , the given quadratic equation has real and equal roots . Thus discriminant must be zero .
=> D = 0
=> 25 - 12p = 0
=> 12p = 25
=> p = 25/12