Question

Solve the quadratic equation 2x+X+y=0 by formula methods​

Answer 1

$\sf{\green{\underline{\underline{\orange{Answer :-}}}}}$

As you can see, I used the Quadratic Formula in each of the original equations, in order to solve for y in terms of x. This gave me equations that I could graph. This technique doesn't come up that often, but it can be a life-saver when you can't seem to solve things any other way.

Oh, and where did those absolute-value bars come from? Recall that, technically, the square root of x2 is the absolute value of x. That's how I did that simplification in the next-to-last line above. And this absolute value will matter shortly.

The absolute value of x in the second equation above gives two cases for the values of y:

If x < 0, then | x | = –x, so y = (x ± 3x)/8 = x/2, – x/4

If x > 0, then | x | = x, so y = (x ± 3x)/8 = – x/4, x/2.

In either case, y = – x/4 or y = x/2.

Since I derived these "y=" solution-equations from the second of the original equations, I will plug them into the first equation to solve for some actual numerical values:

$\sf{\blue{\underbrace{\underline{\orange{HENCE\; VERIFIED✓}}}}}$