Question

What is the sum of all values of k such that the equation 2x^2-kx+8=0 has two distinct integer solutions?

Answer 1

(b²-4ac) > 0

where Z is an integer

(-k)²-4(2)(8) > 0

k²-64 > 0

k²>64

k>8

Therefore the sum of all values of k is infinite

Answer 2

k > 8

Explanation:

Step 1: We know in order for a quadratic equation to have 2 distinct solutions the discriminant has to be positive

Important formula: Discriminant =
`b^(2)-4ac`

Step 2: Input information into discriminant

`b^(2)-4ac` > 0

`k^(2)-4(2)(8)` > 0

`k^(2)-64` > 0

`k^(2)` > 64

`\sqrt{ k^(2)}>√(64)`

k > 8

Therefore in order for the equation to have 2 distinct solutions is to have k > 8