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3 years ago

Please help me with number 2?

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

4 0

The answer to your problem is 2,

Hope this is the correct answer, and hope it helped..

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Step-by-step explanation:

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The roots of 2x^{2} + 3x = 4 are α and β. Find the simplest quadratic equation which has roots <img src="https://tex.z-dn.net/?f

elena-s [515]

$2x^2+3x=4\implies2x^2+3x-4=0\implies x=\dfrac{-3\pm\sqrt{41}}4$

Let $\alpha$ be the root with the positive square root and $\beta$ the root with the negative square root. Then

$\dfrac1\alpha=\dfrac4{-3+\sqrt{41}}\quad\text{and}\quad\dfrac1\beta=\dfrac4{-3-\sqrt{41}}$

The simplest quadratic with these roots can be written as

$\left(x-\dfrac1\alpha\right)\left(x-\dfrac1\beta\right)=x^2-\left(\dfrac1\alpha+\dfrac1\beta\right)x+\dfrac1{\alpha\beta}=x^2-\dfrac34x-\dfrac12$

4 0

3 years ago

Using the order of operations, what should be done first when evaluating this expression?

Nastasia [14]

Answer:

$-\frac{16}{17}\\-0.94117$

Step-by-step explanation:

$\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\left(8\right)}}\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\cdot \:8}}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}=\frac{17}{32}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}\\2\left(9+3\right)-4-3=17\\2\left(9+3\right)-4-3\\2\left(9+3\right)=24\\2\left(9+3\right)\\\mathrm{Add\:the\:numbers:}\:9+3=12\\=2\cdot \:12\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:12=24\\=24-4-3$

$\mathrm{Subtract\:the\:numbers:}\:24-4-3=17\\=\frac{17}{4\cdot \:8}\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:8=32\\=\frac{17}{32}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\\=-\frac{\frac{1}{2}}{\frac{17}{32}}\\\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}\\=-\frac{1\cdot \:32}{2\cdot \:17}\\Refine\\=-\frac{32}{2\cdot \:17}\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:17=34\\=-\frac{32}{34}$

$\mathrm{Cancel\:the\:common\:factor:}\:2\\=-\frac{16}{17}\\\mathrm{Decimal:\quad }\:-0.94117$

3 0

3 years ago