
For what value of k, the roots of the quadratic equation $kx(x - 2\sqrt 5 ) + 10 = 0$ are equal?
Answer
514.5k+ views
Hint: Find the discriminant value and check when it is equal to 0 i.e. D=0.
Complete step-by-step answer:
We have
$
kx(x - 2\sqrt 5 ) + 10 = 0 \to 1 \\
k{x^2} - 2\sqrt 5 kx + 10 = 0 \\
{\text{Given roots are equal then}} \\
D = {b^2} - 4ac = 0 \Rightarrow {b^2} = 4ac \\
\Rightarrow {(2\sqrt 5 k)^2} = 4 \times 10 \times k \\
\Rightarrow 20{k^2} = 40k \\
\Rightarrow 20k(k - 2) = 0 \\
{\text{But k}} \ne 0,{\text{ }}\therefore k = 2 \\
\therefore {\text{ for k = 2 roots of given quadratic equation are equal}}{\text{.}} \\ $
Note: Whether the roots are for real & different, real & equal or imaginary it depends on the value of the discriminant. In this problem we are concerned with discriminant value 0 (which fetches real & equal roots) to get the value of k.
Complete step-by-step answer:
We have
$
kx(x - 2\sqrt 5 ) + 10 = 0 \to 1 \\
k{x^2} - 2\sqrt 5 kx + 10 = 0 \\
{\text{Given roots are equal then}} \\
D = {b^2} - 4ac = 0 \Rightarrow {b^2} = 4ac \\
\Rightarrow {(2\sqrt 5 k)^2} = 4 \times 10 \times k \\
\Rightarrow 20{k^2} = 40k \\
\Rightarrow 20k(k - 2) = 0 \\
{\text{But k}} \ne 0,{\text{ }}\therefore k = 2 \\
\therefore {\text{ for k = 2 roots of given quadratic equation are equal}}{\text{.}} \\ $
Note: Whether the roots are for real & different, real & equal or imaginary it depends on the value of the discriminant. In this problem we are concerned with discriminant value 0 (which fetches real & equal roots) to get the value of k.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What constitutes the central nervous system How are class 10 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE
