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AlexFokin [52]
2 years ago
15

Find the number of terms in this polynomial. 9p2 + 3p − 2

Mathematics
1 answer:
kenny6666 [7]2 years ago
7 0
9p + 3p and 2 -2 that is it
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Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0
3 years ago
Sam bought 2 3/4 pounds of shrimp and 2 1/2 pounds of crabmeat. How much seafood did he buy?
marin [14]
Sam bought 5 1/4 pounds of seafood. 
6 0
3 years ago
Read 2 more answers
X^2 + y^2 =-6x-14-6y
skad [1K]

Answer:

x=−3+√(−y−1)(y+5)

Step-by-step explanation:

thats if your solving for x if not to math w    l   ay

7 0
2 years ago
Justin has a roll of tape 549 centimeters long. he cuts the tape into pieces that are 9 centimeters long. How many 9 centmeter p
Olenka [21]

Answer:

61

Step-by-step explanation:

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2 years ago
David earns $11 an hour. He was scheduled to work 35 hours. However, he picked up an additional 7 hour shift. He is paid double
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You have in total 42 hours so 2 of those hours are double time so you do 40•11 and then add 22•2 (22 is the double time) so you’re answer is $484
7 0
3 years ago
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