Question

⭕Quadratic equation⭕
▶️Find the value of k for which the roots of the quadratic equation kx(x-2)+6=0 are equal.

Answer 1

SEE THE ATTACHMENT
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Answer 2

Question:

Find the value of k for which the quadratic equation kx(x-2) + 6 = 0 has equal roots.

Answer:

k = 6

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 ;

kx(x-2) + 6 = 0

=> kx² - 2kx + 6

Clearly , we have ;

a = k

b = -2k

c = 6

We know that ,

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

=> D = 0

=> (-2k)² - 4•k•6 = 0

=> 4k - 4•6•k = 0

=> 4k•(k - 6) = 0

=> k = 0 , 6

=> k = 6 ( appreciate value )

Hence,

The required values of k is 6 .