The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it's less than 0, there are no solutions. If it's equal to 0, there is one solution.

Step-by-step explanation:

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2 years ago

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Use the discriminant to determine the number of solutions and types of solutions for the quadratic equation, below. Then answer

Setler79 [48]

Answer:

A. Discriminant = 116

B. Number of solutions for the quadratic equation = 2

C. Type of solutions (circle one):Imaginary

D. Type of solutions (circle one):irrational

Step-by-step explanation:

The given quadratic equation is

${x}^{2} + 8x = 13$

We rewrite in standard form to get;

${x}^{2} + 8x - 13 = 0$

The discriminant is

$D = {b}^{2} - 4ac$

where a=1, b=8, c=-13

We substitute to get:

$D = {8}^{2} - 4 \times 1 \times - 13$

$D = 64 + 52$

$D = 116$

Since the discriminant is great than zero, we have two distinct real roots

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2 years ago

Can someone answer this for me

ladessa [460]

The linear equation in standard form is:

6x - 7y = -11

Which is the last option.

<h3>How to get the equation of the line?</h3>

The line in slope-intercept form is written as:

y = a*x + b

We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:

$a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}$

Then we can write:

y = (6/7)*x + b

To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:

-1 = (6/7)*-3 + b

-1 + 18/7 = b

-7/7 + 18/7 = b

11/7 = b

Then the equation is:

y = (6/7)*x + 11/7

If we multiply both sides by 7 we get:

7y = 6x + 11

Now we move the term with "x" to the left:

7y - 6x = 11

That is the line in standard form.

If we multiply both sides by -1, we get the last option:

6x - 7y = -11

If you want to learn more about linear equations:

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1 year ago

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