How do you find the roots, real and imaginary, of $y= x^2 + 4x - 3$ using the quadratic formula?

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How do you find the roots, real and imaginary, of $y= x^2 + 4x - 3$ using the quadratic formula?

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Answer 1 · 2016-02-29T00:10:09

See explanation...

Explanation:

$x^2+4x-3$ is of the form $ax^2+bx+c$ with $a=1$ , $b=4$ and $c=-3$ .

This has zeros given by the quadratic formula:

$x = (-b+-sqrt(b^2-4ac))/(2a)$

$=(-4+-sqrt((-4)^2-(4*1*(-3))))/(2*1)$

$=(-4+-sqrt(16+12))/2$

$=(-4+-sqrt(28))/2$

$=(-4+-sqrt(2^2*7))/2$

$=(-4+-2sqrt(7))/2$

$=-2+-sqrt(7)$

Alternative Method

The difference of squares identity can be written:

$a^2-b^2=(a-b)(a+b)$

Complete the square and use this with $a=x+2$ and $b=sqrt(7)$ as follows:

$x^2+4x-3$

$=x^2+4x+4-7$

$=(x+2)^2-(sqrt(7))^2$

$=((x+2)-sqrt(7))((x+2)+sqrt(7))$

$=(x+2-sqrt(7))(x+2+sqrt(7))$

Hence zeros: $x=-2+-sqrt(7)$

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How do you find the roots, real and imaginary, of $y= x^2 + 4x - 3$ using the quadratic formula?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you find the roots, real and imaginary, of y= x^2 + 4x - 3 y= x^2 + 4x - 3 using the quadratic formula?

1 Answer

Explanation:

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How do you find the roots, real and imaginary, of $y= x^2 + 4x - 3$ using the quadratic formula?