Question

Given that one root is twice the other for the quadratic equation px-3x^2=24 . Find the values of p

Answer 1

Alright, so we can write this as -3x^2+px-24=0 (by subtracting 24 from both sides)

3*-24=-72, so 2 numbers have to add to 72 but multiply to a number p. If a number is y and the other is 2y, that means that y*2y=-72 and 2y^2=72. Therefore, y^2=36 by dividing both sides by 2 and y is either 6 or -6. If y is 6, then 2y is 12 and 6+12=18=p
If y is -6, then 2y=-12 and -6-12=-18=p