Final answer:
To find the roots of the polynomial Q(y) = 12y³ - 28y² - 9y + 10, we can use the quadratic formula. The roots of the polynomial are y = (28 + 4√19) / 24 and y = (28 - 4√19) / 24.
Step-by-step explanation:
To find the roots of the polynomial Q(y) = 12y³ - 28y² - 9y + 10, we can use the factoring method or the quadratic formula. Let's use the quadratic formula:
y = (-b ± √(b² - 4ac)) / 2a
In this case, a = 12, b = -28, and c = 10. Plugging these values into the quadratic formula, we get:
y = (-(-28) ± √((-28)² - 4(12)(10))) / (2(12))
y = (28 ± √(784 - 480))/ 24
y = (28 ± √304) / 24
Simplifying further, we have:
y = (28 ± √(16 * 19)) / 24
y = (28 ± 4√19) / 24
Therefore, the roots of the polynomial are y = (28 + 4√19) / 24 and y = (28 - 4√19) / 24.