No, 1/2 is equivalent to 4/8
Answer:
1 2 real
2. No real
3. 2 Real
4. One real Multiplicity 2.
Step-by-step explanation:
Find the value of the discriminant D (b^2 - 4ac) :-
1 . D = (1)^1 -4 * -3 * 12 = 1 + 144 = 145
D is positive so there re 2 real solutions.
2. D = (-6)^2 - 4*2*5 = 36 - 40 = -4
D is negative so there are NO real solutions.
3. D = (7)^2 - 4 * 1 * -11 = 49 + 44 = 93
2 real
solutions
4. D = (-8)^2 - 4* -1 * -16 = 64 - 64
1 solution. Multiplicity 2.
Answer:
Suppose that you have a square of side length x, the area of this square will be:
A = x^2.
Now, by dynamics, we know that the position of an object that is falling down from a height H, can be written as:
H(t) = (-g/2)*t^2 + H.
We can see a pattern, x^2 is used in both.
Now, profit can be also modeled with quadratic equations, where our objective is to find the maximum of the quadratic (so we can have the maximum profit)
Then the parent function that is useful for gravity, calculating area and profit is the quadratic function:
f(x) = x^2
If (x^2 -10) is one of the factors, that can be further factored into:
(x - sqrt(10) ) * (x+sqrt(10)) =0
making 2 of the 4 solutions equal:
3.1623 and -3.1623
I then used an algebraic long division calculator
http://calculus-calculator.com/longdivision/
to calculate:
<span>x^4 + 5x^3 ‒ x^2 ‒ 50x ‒ 90 divided by x^2 -10 which equals
</span>x^2 + 5x + 9
Using the quadratic formula, the roots of that equation are:
x = -5 + sqrt (-11) / 2
and
x = -5 - sqrt (-11) / 2
Both of those roots are not real.
I tried using online graphing calculators for x^4+5x^3-x^2-50x-90=0 but none worked.
2. For this equation,
<span>3x^2 ‒ 8x + k = 0
I used my OWN quadratic formula calculator
http://www.1728.org/quadratc.htm
and found that real roots no longer exist after "k" is greater than 5.3
</span>