Answer:
No real roots.
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
- Standard Form: ax² + bx + c = 0
- Quadratic Formula:
![x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
<u>Algebra II</u>
Step-by-step explanation:
<u>Step 1: Define</u>
-3x² + 2x = 1
<u>Step 2: Rewrite in Standard Form</u>
- Subtract 1 on both sides: -3x² + 2x - 1 = 0
<u>Step 3: Define</u>
a = -3
b = 2
c = -1
<u>Step 4: Find roots</u>
- Substitute in variables:
![x=\frac{-2\pm\sqrt{2^2-4(-3)(-1)} }{2(-3)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B2%5E2-4%28-3%29%28-1%29%7D%20%7D%7B2%28-3%29%7D)
- Exponents:
![x=\frac{-2\pm\sqrt{4-4(-3)(-1)} }{2(-3)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-4%28-3%29%28-1%29%7D%20%7D%7B2%28-3%29%7D)
- Multiply:
![x=\frac{-2\pm\sqrt{4-12} }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-12%7D%20%7D%7B-6%7D)
- Subtract:
![x=\frac{-2\pm\sqrt{-8} }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B-8%7D%20%7D%7B-6%7D)
Here we see that we cannot take the square root of a negative number. We will get no real roots and only imaginary ones.
Answer:
Step-by-step explanation:
7) 2ab + 4ac = 2*a*b + 2 *2 *a*c
= 2a(b + 2c)
![\dfrac{2ab^{2}c}{2ab+4ac}=\dfrac{2*a* b^{2}*c}{2a(b+2c)}\\\\\\\text{2a in the denominator and numerator get cancelled}\\\\ = \dfrac{b^{2}c}{b+2c}](https://tex.z-dn.net/?f=%5Cdfrac%7B2ab%5E%7B2%7Dc%7D%7B2ab%2B4ac%7D%3D%5Cdfrac%7B2%2Aa%2A%20b%5E%7B2%7D%2Ac%7D%7B2a%28b%2B2c%29%7D%5C%5C%5C%5C%5C%5C%5Ctext%7B2a%20in%20the%20denominator%20and%20numerator%20get%20cancelled%7D%5C%5C%5C%5C%20%3D%20%5Cdfrac%7Bb%5E%7B2%7Dc%7D%7Bb%2B2c%7D)
8) ac - a²c² = c( a - a²c)
bc - abc = c(b - ab)
![\dfrac{ac - a^{2}c^{2}}{bc-abc^{2}}=\dfrac{c(a-a^{2}c)}{c(b-ab)}\\\\](https://tex.z-dn.net/?f=%5Cdfrac%7Bac%20-%20a%5E%7B2%7Dc%5E%7B2%7D%7D%7Bbc-abc%5E%7B2%7D%7D%3D%5Cdfrac%7Bc%28a-a%5E%7B2%7Dc%29%7D%7Bc%28b-ab%29%7D%5C%5C%5C%5C)
![=\dfrac{a-a^{2}c}{b-abc}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7Ba-a%5E%7B2%7Dc%7D%7Bb-abc%7D)
9) b²+ 4b - 5 = b² + 5b - 1b - 5
= b(b + 5) - 1(b + 5)
= (b +5)(b - 1)
b² + 8b + 15 = b² + 5b + 3b + 15
= b(b + 5) + 3(b + 5)
= (b + 5 )(b + 3)
![\dfrac{b^{2}+4b-5}{b^{2}+8b+15}=\dfrac{(b+5)(b-1)}{(b+5)(b+3)}\\\\\\](https://tex.z-dn.net/?f=%5Cdfrac%7Bb%5E%7B2%7D%2B4b-5%7D%7Bb%5E%7B2%7D%2B8b%2B15%7D%3D%5Cdfrac%7B%28b%2B5%29%28b-1%29%7D%7B%28b%2B5%29%28b%2B3%29%7D%5C%5C%5C%5C%5C%5C)
![=\dfrac{b-1}{b+3}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7Bb-1%7D%7Bb%2B3%7D)
That would be -1, -4. since it is in quadrant 3. :)
A) 0 = 100m/s + 2(-9.8)(x_f-0)
x_f = 510
b)
0 = 0 + 100m/s(t) + (1/2)(-9.8)t^(2)
Use the quadratic formula
-200/-9.8 = 20 seconds
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