Question

Find the value of k for which the quadratic equation 2x²-4kx+k=0 has real and equal roots?

Answer 1

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Answer 2

Question:

Find the value of k for which the quadratic equation 2x² - 4kx + k = 0 has real and equal roots.

Answer:

k = 0 , 1/2

Note:

• An equation of degree 2 is know as quadratic equation .

• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.

• The maximum number of roots of an equation will be equal to its degree.

• A quadratic equation has atmost two roots.

• The general form of a quadratic equation is given as , ax² + bx + c = 0 .

• A quadratic equation has atmost two roots .

• The discriminant of the quadratic equation is given as , D = b² - 4ac .

• If D = 0 , then the quadratic equation would have real and equal roots .

• If D > 0 , then the quadratic equation would have real and distinct roots .

• If D < 0 , then the quadratic equation would have imaginary roots .

Solution:

The given quadratic equation is ;

2x² - 4kx + k = 0

Clearly , we have ;

a = 2

b = -4k

c = k

We know that ,

The quadratic equation will have real and equal roots if its discriminant is equal to zero .

=> D = 0

=> (-4k)² - 4•2•k = 0

=> 16k² - 8•k = 0

=> 8k(2k - 1) = 0

=> k(2k-1) = 0

=> k = 0 , 1/2

Hence,

The required values of k are 0 and 1/2 .