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Nastasia [14]
3 years ago
10

Use the discriminant to describe the roots of each equation. Then select the best description.

Mathematics
2 answers:
Bogdan [553]3 years ago
7 0
X2+5x-2=0
a=1, b=5, c=-2

b2-4ac is the discriminant.
(5^2)-4(1)(-2)
25+8=33, so the discriminant is positive

This means there are two real rational roots, so the answer is the second option
grin007 [14]3 years ago
5 0
<h3><u>Explanation</u></h3>
  • Given the equation.

2 =  {x}^{2}  + 5x

  • Arrange the expression into the standard form.

0 =  {x}^{2}  + 5x - 2 \\  {x}^{2}  + 5x - 2 = 0

  • Discriminant

From the standard form equation and from the given equation.

a {x}^{2}  + bx + c = 0 \\ a = 1 \:  \:  \: b = 5 \:  \:  \: c =  - 2

<u>Discriminant</u><u /><u> </u><u>Formula</u>

<u>D =  {b}^{2}  - 4ac</u>

Substitute the value of terms in the discriminant formula.

D =  {(5)}^{2}  - 4(1)(  - 2) \\ D = 25 - 4( - 2) \\ D = 25 + 8 \\ D = 33

<u>Discriminant</u><u> </u><u>Types</u>

D > 0 \:  \:  \:  \: 2 \:  \: real \:  \: roots \\ D = 0 \:  \:  \:  \: 1 \:  \: real \:  \: root \\ D < 0 \:  \:  \: imaginary \:  \: roots

We can rule out the Imaginary root and double root because the discriminant is greater than 0. Therefore, the only choices are either Irrational or Rational.

However, we cannot factor the expression by using two brackets or common factor. We can say that the equation has two real irrational roots.

<h3><u>Answer</u></h3>
  • real and irrational root
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What is the solution set of {x | x &lt; -3} ∩ {x | x &gt; 5}
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3 years ago
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6 0
3 years ago
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Use a net to find the surface area of the right triangular prism shown:
vazorg [7]

The surface area of the right triangular prism is 270 sq ft

<h3>Total surface ara of the prism</h3>

The total surface area of the prism is the  sum of all the area of its faces

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3 0
2 years ago
Please Please Please help me with the answer
Tems11 [23]

c = amount of chocolate donuts

m = amount of maple donuts.

so we know the total in all is 41 donuts, thus c + m = 41.

we also know that whatever c is, m is 25 fewer than that, m = c - 25.

\bf \begin{cases} c+m=41\\ \boxed{m}=c-25\\ --------\\ c+\boxed{c-25}=41 \end{cases} \\\\\\ 2c-25=41\implies 2c=66\implies c=\cfrac{66}{2}\implies c=33 \\\\\\ \stackrel{\textit{since c = 33}}{m = c - 25}\implies m=33-25\implies m = 8

6 0
3 years ago
Read 2 more answers
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