Question

Qn: How many integer values?
If x2 + kx - 72 = 0 has
integer roots, how many integer values can ik
takes ?​

Answer 1

Step-by-step explanation:

As it is similar to ax2 + bx + c, the product of roots = c/a, here c/a= -72.

If, -72 can be written as product of 2 integers, e.g. x and y, then sum of roots = x+y = -b/a = -k

If (x,y) = (-72,1), then x+y (-k) = -71,

If (x,y) = (72,-1), then x+y = 71,

Similarly, (x,y) can be (36,-2),(-36,2),(24,-3),(-24,3),(18,-4),(-18,4),(12,-6),(-12,6),(9,-8),(-9,8)

So, total is 12.

Imo. E

As it is similar to ax2 + bx + c, the product of roots = c/a, here c/a= -72.

If, -72 can be written as product of 2 integers, e.g. x and y, then sum of roots = x+y = -b/a = -k

If (x,y) = (-72,1), then x+y (-k) = -71,

If (x,y) = (72,-1), then x+y = 71,

Similarly, (x,y) can be (36,-2),(-36,2),(24,-3),(-24,3),(18,-4),(-18,4),(12,-6),(-12,6),(9,-8),(-9,8)

So, total is 12.

Imo. E