Find the roots of the parabola given by the following equation.
2x^2+ 5x - 9 = 2x
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ANSWER

EXPLANATION

We want to find the roots of the parabola with equation:

We need to write this in the standard quadratic equation form.

We group all terms on the left to get:

We simplify to get:

We now compare to:

The factors of -18 that sums up to 3 are -3, 6.

We split the middle term with these factors to get:

Factor by grouping:

Factor again to obtain:

Apply the zero product principle to get:

one of each metals

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form