Question

For what value(s) of p will the quadratic
equationpx2 + 4x + 1 = 0 have real root?​

Answer 1

Answer :

p ≤ 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 ;

px² + 4x + 1 = 0

Now ,

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

a = p

b = 4

c = 1

Now ,

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

=> D = b² - 4ac

=> D = 4² - 4•p•1

=> D = 16 - 4p

Also ,

The given quadratic equation will have real roots if its discriminant is greater than or equal to zero .

Thus ,

=> D ≥ 0

=> 16 - 4p ≥ 0

=> 16 ≥ 4p

=> 4p ≤ 16

=> p ≤ 16/4

=> p ≤ 4

Hence , p ≤ 4 .