Answer:
Step-by-step explanation:
Theorm-The Fundamental Theorem of Algebra: If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.
Let's verify that the Fundamental Theorem of Algebra holds for quadratic polynomials.
A quadratic polynomial is a second degree polynomial. According to the Fundamental Theorem of Algebra, the quadratic set = 0 has exactly two roots.
As we have seen, factoring a quadratic equation will result in one of three possible situations.
graph 1
The quadratic may have 2 distinct real roots. This graph crosses the
x-axis in two locations. These graphs may open upward or downward.
graph 2
It may appear that the quadratic has only one real root. But, it actually has one repeated root. This graph is tangent to the x-axis in one location (touching once).
graph 3
The quadratic may have two non-real complex roots called a conjugate pair. This graph will not cross or touch the x-axis, but it will have two roots.
Initial number = 36
Final number = 63
Change in number = 63 - 36
= 27
Percentage change = (27/36) * 100
= (3/4) * 100
= 3 * 25
= 75 percent
So the percentage change from 36 to 63 is 75%. I hope the procedure for solving is absolutely clear for you to understand. In future you can attempt such problems by following the procedure shown and you will require no further help from outside. Just be careful about the numerator and the denominator.
Answer:
2 solutions
Step-by-step explanation:
I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...
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To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:
3x(x -4) +5 -x -(2x -7) = 0
3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses
3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms
3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor
The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.
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<em>Alternate method</em>
Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...
d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c
d = (-15)^2 -4(3)(12) = 225 -144 = 81
This positive value means the equation has 2 real solutions.
Answer:
free point 3.3.3 points sorry but I just need
If you divide decimals you have to bring up the decimal point but if you divide whole numbers you dont have any decimal points so you just divide the numbers. Sorry if i didnt help i just wanted to help.
