The roots of the equation x²-kx+28=0 are alpha (a) and alpha (a) + 3.find the values of k.

Solution:

Given that equation is:

Roots are:

To find: value of x

The general quadratic equation is:

From given,

a = 1

b = -k

c = 28

Therefore,

Given roots are:

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, sum of roots are:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11