How do you find the discriminant of $7 x^{2} + 6 x + 2 = 0$ $7x^2+6x+2=0$ and use it to determine if the equation has one, two real or two imaginary roots?

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How do you find the discriminant of $7 x^{2} + 6 x + 2 = 0$ $7x^2+6x+2=0$ and use it to determine if the equation has one, two real or two imaginary roots?

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Answer 1 · 2017-03-18T13:15:12

$7 x^{2} + 6 x + 2$ $7x^2+6x+2$ has complex number roots

Explanation:

Consider the standard format of $y = a x^{2} + b x + c$ $y=ax^2+bx+c$

Where $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x=(-b+-sqrt(b^2-4ac))/(2a)$

The discriminant is the part of $b^{2} - 4 a c$ $b^2-4ac$

If this is 0 then the vertex is actually on the on the axis so has 1 point

If this is negative then the roots are complex numbers

If this is positive and greater than 0 then it has two roots
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Added comment: I have had people argue that when the discriminant is 0 there is still 2 roots but they are the same value. This condition is called duplicity.
I do not like this!
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So for this equation:

Discriminant $\to b^{2} - 4 a c = {(6)}^{2} - 4 (7) (2) = 36 - 56 < 0$ $-> b^2-4ac = (6)^2-4(7)(2) = 36 -56 <0$

So $7 x^{2} + 6 x + 2$ $7x^2+6x+2$ has complex number roots

Answer 2 · 2017-03-18T13:15:32

The solutions are $S = {- \frac{3}{7} + \frac{\sqrt{5}}{7} i, - \frac{3}{7} - \frac{\sqrt{5}}{7} i}$ $S={-3/7+sqrt5/7i,-3/7-sqrt5/7i}$

Explanation:

The quadratic equation is

$a x^{2} + b x + c = 0$ $ax^2+bx+c=0$

Here, we have

$7 x^{2} + 6 x + 2 = 0$ $7x^2+6x+2=0$

The discriminant is

$Delta=b^2-4ac=36-4*7*2=36-56=-20$

As $Delta<0$ , there are no real roots.

The roots are imaginary

$x=(-b+-sqrtDelta)/(2a)$

$x=(-6+-i2sqrt5)/(14)$

$x_1=-3/7+sqrt5/7i$

$x_2=-3/7-sqrt5/7i$

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How do you find the discriminant of $7 x^{2} + 6 x + 2 = 0$ $7x^2+6x+2=0$ and use it to determine if the equation has one, two real or two imaginary roots?

2 Answers

Explanation:

Explanation:

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Science

Math

Humanities

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How do you find the discriminant of 7x^2+6x+2=07x2+6x+2=07x^2+6x+2=0 and use it to determine if the equation has one, two real or two imaginary roots?

2 Answers

Explanation:

Explanation:

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How do you find the discriminant of $7 x^{2} + 6 x + 2 = 0$ $7x^2+6x+2=0$ and use it to determine if the equation has one, two real or two imaginary roots?