Final answer:
The student's question seems to contain a possible typographical error. It's about solving a quadratic equation, but without the correct formulation or additional context, we cannot provide a definitive answer. Correct solving would involve using the quadratic formula.
Step-by-step explanation:
The student is asking to solve a given quadratic equation, ap² + bp² = 20a, with specific values for ‘a’ and ‘b’ given points (2,0) and (0,4). The solution involves matching the equation to the standard form at² + bt + c = 0 and finding the appropriate value of ‘a’ and ‘b’ that satisfy the condition. However, the provided information seems out of context, but typically, the quadratic formula is used to find the roots of a quadratic equation which is given by:
t = -b ± √(b² - 4ac) / (2a)
Though the original expression cannot be solved with the provided details, when dealing with a standard quadratic equation, one would plug the known values into the quadratic formula to find the variable.