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hjlf
3 years ago
11

Please help solve quick

Mathematics
1 answer:
RoseWind [281]3 years ago
5 0

Answer:

see below

Step-by-step explanation:

3x^2 + 17x +10 =0

(3x+   ) ( x+   ) =0

We need to factor 10  = 2*5  or 1*10

They are positive since we have all positive terms

3*5 = 15+2 = 17

The 5 needs to multiply the 3 so it goes on the outside

(3x+   ) ( x+  5 ) =0

That leaves the 2 on the inside

(3x+ 2  ) ( x+ 5  ) =0

Using the zero product property

3x+2 =0     x+5=0

3x = -2          x=-5

x = -2/3          x = -5

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See attached. (Both inequalities graph to the same region.)

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To graph an inequality, you first replace the inequality symbol by an equal sign. Then you graph the line (or curve) described by the equation. If the inequality symbol includes the "or equal to" case, then the line (or curve) is solid and is part of the solution set. If not, then the line (or curve) is dashed and is <em>not part of the solution set</em>.

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_____

After you have graphed the boundary of the solution region, you need to determine which side of the boundary has the solutions. I find it easy to do this by locating an x- or y-term with a positive coefficient and seeing which side of the inequality symbol that lies on. Here, both the x-term and the y-term lie on the "is greater than" side of the symbol, so the half-plane is shaded above and to the right of the line, where x- and y-values are greater than they are on the line.

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The graph seems to show only one equation. Both are there, but the dashed blue line sits on top of the dashed red line, so you can't see it. The purple shading indicates both red and blue shading in the same area.

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