Please help this is freaking me out

Question

What is the nature of the roots for y = x ^ 2 - 10x + 25 ? Explain your answer

Answer 1

What is the nature of the roots for y = x ^ 2 - 10x + 25 ? Explain your answer

The factors are (x - 5)(x -5), so there is a "double root" at x = 5. For most of us, that simply means that the answer is x = 5 (I've never heard an explanation of when and why double roots are significant.

Answer 2

The discriminate is 100-4(25)=0 That means just one real root, or you can say it repeats, so you get the same real root twice. When the discriminate = 0 that's what happens.

The discriminate is b²-4ac. With this quadratic equation b=-10, a=1 c=25

Graph it and it just touches the x-axis once. It's a parabola with its vertex touching the x-axis

Factor the equation y=(x-5)² That's two factors (x-5) and (x-5). Set each = 0, solve for x. x=5 and 5 again.

The point (5,0) is the parabola's vertex, it's minimum point, the only place the parabola touches the x-axis

5 is the real root, or zero. It repeats once. 5 and 5, as quadratic equations always have 2 roots, sometimes 2 real, sometimes 1 real that repeats, , sometimes 2 imaginary roots. That corresponds to a parabola intersecting the x-axis twice, once or never.