Question

Find the value of k for which the root of the quadratic equation kx²-10x+5=0 are 2 equal

Answer 1

so the value of k is 5.

Answer 2

Question:

Find the value of k for which the quadratic equation kx² - 10x + 5 = 0 has equal roots.

Answer:

k = 5

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 .

• 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 ;

kx² - 10x + 5 = 0

Clearly , we have ;

a = k

b = - 10

c = 5

We know that ,

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

=> D = 0

=> (-10)² - 4•k•5 = 0

=> 100 - 20k = 0

=> 20k = 100

=> k = 100/20

=> k = 5

Hence,

The required values of k is 5 .