Final answer:
The quadratic function P(x)=3x²−7x+10 does not have real zeroes because the discriminant is negative, which means the solutions are complex numbers.
Step-by-step explanation:
To determine the zeroes of the quadratic function P(x)=3x²−7x+10, we can use the quadratic formula, which is given by:
x = −b ± √(b² − 4ac) / (2a)
For P(x)=3x²−7x+10, the coefficients are: a=3, b=−7, and c=10. Plugging these into the quadratic formula:
x = (7 ± √(49 − 4 * 3 * 10)) / (2 * 3)
x = (7 ± √(49 − 120)) / 6)
x = (7 ± √(−71)) / 6)
Because the discriminant (−71) is negative, this means the quadratic function does not have real zeroes. Instead, the solutions are complex numbers, and thus none of the given options a) to d) are correct.