Final answer:
The zeros of the quadratic equation Y1 = 6x² + 5x - 8 are found using the quadratic formula. After substituting values for a, b, and c into the formula, the resulting calculations will provide the two irrational zeros of the equation.
Step-by-step explanation:
To find the zeros (x-intercepts) of the quadratic equation Y1 = 6x² + 5x − 8, we can use the quadratic formula, which is derived from the standard form of a quadratic equation ax² + bx + c = 0. The quadratic formula is given by:
x = −b ± √(b² − 4ac) / (2a)
In this case, a = 6, b = 5, and c = −8. Plugging these values into the quadratic formula:
x = −5 ± √(5² − 4×6×(−8)) / (2×6)
x = −5 ± √(25 + 192) / 12
x = −5 ± √217 / 12
Since 217 is not a perfect square, we will have two irrational zeros. To complete the calculation, we need to find the approximate values of these zeros by calculating the square root of 217.