Math, asked by patelrivraj, 6 months ago

for what value of k quadratic equations kx^2-5x+k has two equal roots​

Answers

Answered by AlluringNightingale
0

Answer :

k = ± 5/2

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 ;

kx² - 5x + k = 0

Now ,

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

a = k

b = -5

c = k

Now ,

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

=> D = b² - 4ac

=> D = (-5)² - 4•k•k

=> D = 25 - 4k²

Also ,

It is given that , the given quadratic equation has real and equal roots . Thus , its discriminant must be zero .

Thus ,

=> D = 0

=> 25 - 4k² = 0

=> 4k² = 25

=> k² = 25/4

=> k = √(25/4)

=> k = ± 5/2

Hence , k = ± 5/2 .

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