write a quadratic equation whose roots are 6 and 4 and leading coefficient is 2

Question

use letter x to represent variable

Answer 1

If the roots are 4 and 6, then its factors are (x - 4) and (.x - 6).

the leading coefficient does not change the roots.

So, y = 2(x - 4)(x - 6) which can also be written as"

y = 2x² - 20x + 48

Note that the axis of symmetry is the line x = k where k is the average of the roots.

Check it out here:

desmos.com/calculator/ncdiq8pbwz

Use the slider on A to see that indeed the roots do not change (A cannot equal 0).