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3 years ago

Determine what type of number the solutions are and how many exist for the equation 3x^2+7x+5=0

Mathematics

1 answer:

Hitman42 [59]3 years ago

6 0

Answer:

Two complex (imaginary) solutions.

Step-by-step explanation:

To determine the number/type of solutions for a quadratic, we can evaluate its discriminant.

The discriminant formula for a quadratic in standard form is:

$\Delta=b^2-4ac$

We have:

$3x^2+7x+5$

Hence, a=3; b=7; and c=5.

Substitute the values into our formula and evaluate. Therefore:

$\Delta=(7)^2-4(3)(5) \\ =49-60\\=-11$

Hence, the result is a negative value.

If:

The discriminant is negative, there are two, complex (imaginary) roots.
The discriminant is 0, there is exactly one real root.
The discriminant is positive, there are two, real roots.

Since our discriminant is negative, this means that for our equation, there exists two complex (imaginary) solutions.

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B. Somewhere between years 11 and 12 they had the same width.

C. You can place the values on a graph and connect the points, and look at the intersections to determine points in time where they were of the same width.

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To determine the exact point in time where they meet we would need to draw a graph, with the width in feet on the X axis and the year on the Y axis. Then we place all the pairs in the graph by their coordinates, and connect the points that correspond to each beach. We then see where the lines intersect and use mathematics to determine the values of X and Y, giving us the time and width when the two beaches were equal.

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