How do you find the roots, real and imaginary, of $y= 5x^2 - 245$ using the quadratic formula?

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Answer 1 · 2017-10-26T16:48:08

See a solution process below:

First, we can rewrite this equation as:

$y = 5x^2 + 0x - 245$

To find the roots we need to set the right side of the equation equal to $0$ and solve for $x$ :

$5x^2 + 0x - 245 = 0$

We can now use the quadratic equation to solve this problem:

For $color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0$ , the values of $x$ which are the solutions to the equation are given by:

$x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))$

Substituting:

$color(red)(5)$ for $color(red)(a)$

$color(blue)(0)$ for $color(blue)(b)$

$color(green)(-245)$ for $color(green)(c)$ gives:

$x = (-color(blue)(0) +- sqrt(color(blue)(0)^2 - (4 * color(red)(5) * color(green)(-245))))/(2 * color(red)(5))$

$x = +- sqrt(0 - (-4900))/10$

$x = +- sqrt(0 + 4900)/10$

$x = +- sqrt(4900)/10$

$x = -70/10$ and $x = 70/10$

$x = -7$ and $x = 7$

How do you find the roots, real and imaginary, of y= 5x^2 - 245 y= 5x^2 - 245 using the quadratic formula?