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VLD [36.1K]
3 years ago
6

If two zeroes of a polynomial x3+5x2+7x+3 are -1 and-3 then find the third Zero

Mathematics
1 answer:
belka [17]3 years ago
7 0

Answer:

Third zero is -1.

Step-by-step explanation:

consider the given polynomial is  

P(x)=x^3+5x^2+7x+3

It is given that -1 and -3 are two zeroes, therefore (x+1) and (x+3) are two factors of given polynomial.

The given polynomial can be rewritten as

P(x)=x^3+x^2+4x^2+4x+3x+3

P(x)=x^2(x+1)+4x(x+1)+3(x+1)

P(x)=(x+1)(x^2+4x+3)

Now, splitting the middle term, we get

P(x)=(x+1)(x^2+3x+x+3)

P(x)=(x+1)(x(x+3)+1(x+3))

P(x)=(x+1)(x+1)(x+3)

P(x)=(x+1)^2(x+3)

Here, power of (x+1) is 2. It means the multiplicity of zero -1 is 2.

So, three zeroes are -1, -1 and -3.

Therefore the third zero is -1.

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For 5 points and brainliest to the best correct answer, find the missing measures.<br> Thank you
zzz [600]

Answer:

  • x = 7
  • y = 97°
  • z = 19

Step-by-step explanation:

The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.

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Angle y forms a linear pair with the one marked 83°, so is supplementary to it:

  y = 180°-83° = 97°

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The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.

  (7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle

  10x +27 = 97 . . . . . . . collect terms

  10x = 70 . . . . . . . . subtract 27

 x = 7 . . . . . . . . divide by 10

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The side marked Z is congruent to the opposite parallel side, so ...

  z = 19

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The missing measures are ...

  • x = 7
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<em>Additional comment</em>

You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...

  (7x -5) +(3x +32) +83 = 180

Subtracting 83° from both sides gives the equation we used above.

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2 years ago
Given: f(x) = 2x + 5 and g(x) = x2 and h(x) = -2x<br><br> h(g(f(x)))
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Hello here is a solution :
<span>h(g(f(x))) ?

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Use the given figure to solve the remaining parts of the triangle AIR.
PIT_PIT [208]

<u><em>Answer:</em></u>

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<u><em>Step-by-step explanation:</em></u>

In the given problem, you can solve the unknown side of the triangle using either<em> Pythagorean Theorem</em> or<em> SOA CAH TOA</em> method.<em> </em><em>In Trigo, you can use the Pythagorean Theorem if the triangle has 90 degrees, or it is a right triangle.</em>

In the given problem, the angle of the triangles are unknown, therefore to solve the unknown side of triangles, we will you use the SOA CAH TOA.

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Lets provide the solution for the number, and the rest have the same solutions and process.

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Cosu= 17/23, to get the angle, use inverse cosine.

The result will be 42.34°, and to get the unknown side, use TOA

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It will give you 15.49 cm

In the number 2 and 5, it will be the same when you rotate the triangle.

Read more about the concept of SOA CAH TOA at

<em>brainly.com/question/22767551</em>

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<u><em>#BrainlyFast</em></u>

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