The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).
<h3>How to determine the characteristics of the roots of a quadratic equation by discriminant</h3>
Herein we have a <em>quadratic</em> equation of the form a · x² + b · x + c = 0, whose discriminant is:
d = b² - 4 · a · c (1)
There are three possibilities:
- d < 0 - <em>conjugated complex</em> roots.
- d = 0 - <em>equal real</em> roots (real and rational root).
- d > 0 - <em>different real</em> roots (real and irrational root).
If we know that a = 3, b = 7 and c = - 2, then the discriminant is:
d = 7² - 4 · (3) · (- 2)
d = 49 + 24
d = 73
The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).
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Answer:
qn 10. 15mn² - 23m²n +4m³
Step-by-step explanation:
1. distribute 4m through the parenthesis
8mn² - 12m²n + 4m³ - 2n(5m² - 3nm) + nm(n-m)
2. use the commutative property to reorder the terms
8mn² - 12m²n + 4m³ - 2n(5m² - 3mn) + mn(n - m)
3. distribute -2n through the remaining parenthesis
8mn² - 12m²n + 4m³ -10m²n + 6mn² + mn² - m²n
4. collect like terms
8mn² + 6mn² + mn² - 12m²n - 10m²n - m²n + 4m³
5. complete bodmas
15mn² - 23m²n +4m³
that's is how you do it so the answer is
15mn² -23m²n + 4m³
To generate the equation we set up the factors
(x+3) * (x-1) * (x-2) which equals
x^2 + 2x -3 * (x-2)
x^3 +2x^2 -3x -2x^2 -4x +6 equals
x^3 -3x -4x +6 which equals
x^3 -7x +6
Answer:
t = 4 h
Step-by-step explanation:
Painter A initial fee 40 $ and each hour charge 45 $
Painter B initial fee 100 $ and each hour charge 30 $
The equations for painters are straight lines.
The initial fee is the intercept of the line with the y-axis ( painters receive 40 and 100 $ respectively and they have done nothing.
The equation for a straight line is:
y = m*x + b where m is the slope and b the intercept with the y-axis
Then
Painter A when x = 0 y = b = 40
And each hour of work cost 45 $ then f x = t in hours
The equation for Painter A is y = 45*t + 40
Similarly, the equation for Painter B is
y = 30*t + 100
We have a two equations system, the solution will indicate when the two painters will charge the same amount of money
y = 45*t + 40 (1)
y = 30*t + 100 (2)
Equation 1 - equation 2
0 = 15*t - 60
15*t = 60
t = 60/15
t = 4 h
Answer:
1/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-17 - (-8) / -5 - 13
-9 / - 18
= 1/2
