Yes, a polynomial can have four solutions (roots) but only two x-intercepts if it has repeated roots, such as a polynomial expressed as \((x - a)^2(x - b)^2\), where \(a\) and \(b\) are distinct real numbers, resulting in the x-axis being touched at \(x = a\) and \(x = b\) but not crossed.
Can a polynomial have four solutions but only two x-intercepts? In 1 sentences, explain how this can or cannot occur.
3 answers
answer like a highschooler
Yes, a polynomial can have four solutions but only two x-intercepts if it has repeated roots; for example, if it looks like \((x - 2)^2(x - 3)^2\), it touches the x-axis at \(x = 2\) and \(x = 3\) but doesn't cross it, which means it counts as two intercepts even though there are four solutions.