For the quadratic 2x^2 - 3x - 2 = 0 with roots α and β, α + β equals what?

For the quadratic 2x^2 - 3x - 2 = 0 with roots α and β, α + β equals what?

• A. -a/b
• B. 3/2
• C. a/b
• D. -3/2

Answer: (B)

The sum of the roots of a quadratic is given by −b/a. For the quadratic 2x^2 − 3x − 2 = 0, the leading coefficient a is 2 and the x-coefficient b is −3. So α + β = −(−3)/2 = 3/2. This matches the value 3/2, which is the correct result. The other simple ratios you might think of, like −a/b or a/b, do not give the sum (for example −a/b = 2/3 and a/b = −2/3), and b/a would be −3/2, not the sum.

The sum of the roots of a quadratic is given by −b/a. For the quadratic 2x^2 − 3x − 2 = 0, the leading coefficient a is 2 and the x-coefficient b is −3. So α + β = −(−3)/2 = 3/2. This matches the value 3/2, which is the correct result. The other simple ratios you might think of, like −a/b or a/b, do not give the sum (for example −a/b = 2/3 and a/b = −2/3), and b/a would be −3/2, not the sum.