If a = 2 and c = 6 in the quadratic ax^2 + bx + c = 0, what is the product of the roots?

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Multiple Choice

If a = 2 and c = 6 in the quadratic ax^2 + bx + c = 0, what is the product of the roots?

Explanation:
The product of the roots comes from how a quadratic is built from its roots. If the roots are r1 and r2, then ax^2 + bx + c = a(x - r1)(x - r2) expands to ax^2 - a(r1 + r2)x + a r1 r2. The constant term is c, which equals a r1 r2, so the product r1 r2 = c/a. With a = 2 and c = 6, the product is 6/2 = 3. So the roots multiply to 3. The other values would require a different c/a ratio.

The product of the roots comes from how a quadratic is built from its roots. If the roots are r1 and r2, then ax^2 + bx + c = a(x - r1)(x - r2) expands to ax^2 - a(r1 + r2)x + a r1 r2. The constant term is c, which equals a r1 r2, so the product r1 r2 = c/a.

With a = 2 and c = 6, the product is 6/2 = 3. So the roots multiply to 3. The other values would require a different c/a ratio.

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