exam Maths Puzzle Numerical Ability

Hello. Please help me ASAP- I need to turn this in quick. So I have a worksheet that says that I need to discriminate the solutions of the quadratic equation: x squared + 5x + 3 + a. How do I do it and what does the direction mean?

Thanks.

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The price is now $500. What was the original price if the discount is 4%? if one third of a number is 6 less than half of the number, what is the number?