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mojhsa [17]
2 years ago
10

When Brianna plays solitaire, she keeps track of how many times she wins and loses. She has won

Mathematics
1 answer:
Lady bird [3.3K]2 years ago
7 0
Brianna has played 27 games in total
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4 years ago
The quadratic equation 8x²+12x-14 has two real roots. What is the sum of the squares of these roots?
mars1129 [50]

Answer:

The real roots are

x=\frac{(-3+\sqrt{37})}{4} and x=\frac{(-3-\sqrt{37})}{4}

The sum of the squares of these roots is \frac{-3}{2}

Step-by-step explanation:

The given quadratic equation is 8x^2+12x-14 has two real roots.

To find the roots .

8x^2+12x-14=0

Dividing the above equation by 2

\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}

4x^2+6x-7=0

For quadratic equation ax^2+bx+c=0 the solution is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Where a and b are coefficents of x^2 and x respectively, c is a constant.

For given quadratic equation

a=4, b=6, c=-7

x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}

=\frac{-6\pm\sqrt{36+112}}{8}

=\frac{-6\pm\sqrt{148}}{8}

=\frac{-6\pm\sqrt{37\times 4}}{8}

=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}

=\frac{-6\pm\sqrt{37}\times 2}{8}

=2\frac{(-3\pm\sqrt{37})}{8}

=\frac{-3\pm\sqrt{37}}{4}

x=\frac{(-3\pm\sqrt{37})}{4}

The real roots are

x=\frac{(-3+\sqrt{37})}{4} and x=\frac{(-3-\sqrt{37})}{4}

Now to find the sum of the squares of these roots

\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}

=\frac{-6}{4}

=\frac{-3}{2}

\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}

Therefore the sum of the squares of these roots is \frac{-3}{2}

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Population education is included in school curriculum because of following reasons: It aware the causes and consequences of population growth on socio-economic and environmental aspect. It imparts the knowledge and changes the attitudes and practice of people regarding population.

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Which graph represents the solution set for the inequality x ≤ 18?
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You didn't include any graphs but what you're looking for is a solid vertical line on x = 18 or the ordered pair (18, 0) where the whole left side of the line is shaded. 

EDIT: I said whole left side of the graph; changed it to "line"
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