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secondary 3 | A Maths

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Therefore, a = 1, b = (2 - k), c = k.

We will now study the quadratic formula, which is -b +- √(b^2 - 4ac) divided by 2.

If √(b^2 - 4ac) = 2, then one root will be -b/2 + 1, and the other root will be -b/2 -1.

The difference between the roots is 2, which is what we are aiming for.

Hence, b^2 - 4ac = 4.

We know the values of a, b and c, so place them in:

(2 - k)^2 - 4k = 4

Expand:

k^2 - 8k + 4 = 4

Subtract 4 on both sides:

k^2 - 8k = 0

We can factorize:

k(k - 8) = 0

k = 0 or k = 8

The roots will be -b/2 +- 1, which is:

-(2 - k)/2 +- 1

When k = 0, the roots are -2, 0.

When k = 8, the roots are 2, 4.

However, we know the quadratic equation has non-zero roots. So k = 0 is rejected.

The final answer is k = 8, the roots are 2, 4.

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