Question

The difference between the roots is x2-13x+k=0 is 17 find k

Answer 1

Answer: k= -30

Step-by-step explanation:

Given, The difference between the roots is x2-13x+k=0 is 17

a = 1, b= -13, c= k

Let m & n be it's roots and m>n

Then A/q, m- n = 17........(1)

Also, sum if roots, m+n = -b/a

m+n= -(-13) /1

m+ n = 13.........(2)

Adding equations (1) & (2), we get

m - n + m+n = 17 + 13

2m = 30

So, m= 15

Put m= 15, in equation (1)

15-n= 17

n= 15-17= -2

Also, product of roots = c/a

m×n = c/a

15×(-2) = k

-30= k