x cube minus 3 x minus 2 Greater than or equal to zero
Answers
Answer:
Section 1-6: Solving Quadratic Equations
Any equation in the form
ax2 + bx + c = 0 with a not equal 0
is called a quadratic equation!
A value that satisfies this equation is called a root, zero or solution of the equation!! We have three methods we can use to solve these equations:
1) factoring (easy)
2) completing the square
3) quadratic formula
Factoring review!
Solve each by factoring
1) x2 + 4x -5 = 0
Solution: factor (x + 5)(x - 1) = 0
Therefore, x = -5 or x = 1
2) (3x - 2)((x + 4) = -11
Solution: Foil first 3x2 + 10x - 8 = -11
Put in correct form 3x2 + 10x + 3 = 0
factor (3x + 1)(x + 3) = 0
Solution: x = -1/3 or x = -3
Completing the square!!
Follow the explanation and sample problem to review completing the square
1) Use completing the square to find the solutions for:
2x2 - 12x - 9 = 0
Solution:
Move the constant to the other side: 2x2 - 12x = 9
Divide by the coefficient of x2 x2 - 6x = 9/2
Take half the coefficient of x and square: x2 - 6x + 9 = 9/2 + 9
Factor the trinomial square: (x - 3)2 = 27/2
Take the square root of both sides:
Simplify the radical:
Isolate for x:
Quadratic Formula
As proved in class the quadratice formula is derived by completing the square. Here is the formula:
If ax2 + bx + c = 0 then the roots of the equation are:
Look familiar? It better!!
Solve the following problem by using the quadratic formula.
2x2 + 5 = 3x
2x2 - 3x + 5 = 0 (putting in correct form)
a = 2, b = -3 and c = 5 Use the formula:
Step-by-step explanation:
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