Question

find the value of k for which roots of the quadratic equation k x square - 14 x + 8 = 0 are equal

Answer 1

here's your answer dude.
given:- roots are equal therefore x=0
put x=0 in following quadratic equation
kx(square)-14x+8=0
k×0(square)-14×0+8=0 since roots are equal
k=-8

Answer 2

Question:

Find the value of k for which the quadratic equation kx² - 14x + 8 = 0 has equal roots.

Answer:

k = 49/8

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 - 14x + 8 = 0

Clearly , we have ;

a = k

b = -14

c = 8

We know that ,

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

=> D = 0

=> (-14)² ,- 4•k•8 = 0

=> 4•49 - 4•8k = 0

=> 4(49 - 8k) = 0

=> 49 - 8k = 0

=> 8k = 49

=> k = 49/8

Hence,

The required values of k is 49/8 .