0

Working on a ACT practice problem with my son.

In the equation x^2 + px + k = 0, p and k are integers. The only possible value for x is 4. What is the value of p?

I think the fact that it says p and k are integers are key to solving this problem, I just can't figure out why. Does it have something to do with the fact that p = m + n and k = m * n?

What kind of problem is this so we can study further?

polyhedron
  • 117
  • 1
    $(x-4)^2 = x^2 - 8x+16$ – Will Jagy Dec 08 '20 at 01:24
  • Consider the graph of $y=x^2+px+k$. What does it mean graphically if there's exactly one value of $x$ such that $y=0$? – PM 2Ring Dec 08 '20 at 01:25
  • But yes, you were on the right track. Also see https://en.wikipedia.org/wiki/Vieta%27s_formulas – PM 2Ring Dec 08 '20 at 01:26
  • 2
    Given that this question is practice for the ACT (taken in high school for college admissions), all you need is the fact that $x = 4$ and the quadratic formula: $$x= \frac{-p \pm \sqrt{p^2- (4)(1)(k)}}{2}.$$ Since there is only one value for $x$, we know that $p^2- 4k = 0$. This tells us $p= -8, k=16$. – amWhy Dec 08 '20 at 01:34

0 Answers0