Answer:
Standard Form a b c
- 2x² - x + 5 = 0 2 -1 5
- x² + 4x - 5 = 0 1 4 -5
- x² - 3x = 0 1 -3 0
- y² + y+ 5 = 0 1 1 5
- 5x² - 7x = 0 5 -7 0
- 3x² - 2x + 4 = 0 3 -2 4
- x² + 3x = 0 1 3 0
- x² - 4x - 5 = 0 1 -4 -5
- x² + 2x + 8 = 0 1 2 8
- x² - x + 15 = 0 1 -1 15
Examples to solve some on your own:
Quadratic equations are of the form:
<em>ax</em><em>²</em><em> </em><em>+</em><em> </em><em>bx</em><em> </em><em>+</em><em> </em><em>c</em><em> </em><em>=</em><em> </em><em>0</em>
In their standard form you'll have to place the variables in their decreasing order of exponents, like:
- x raised to 2, first
- then x raised to 1
- a finally x raised to 0 (since x⁰ = 1, every constant is assumed to be with x⁰)
<u>In the very first question,</u> we have:
x = 2x² + 5
we'll want 0 on one side and exponents in their decreasing order on the other
taking x to the RHS (it's sign gets reversed, when moving from one side to another)
0 = 2x² - x + 5 . . . . .(¡¡)
so this is the standard form!
comparing this equation with ax² + bx + c = 0 . . . . .(¡)
we get,
<em>(a is with x² in eqn. (¡) and 2 is with x² in eqn. (¡¡) so a will be equal to 2)</em>
<u>I</u><u>n the 10th question:</u>
=> 2x - 5(x + 3) = x(x - 4)
removing the parenthesis:
=> 2x - 5x - 15 = x² - 4x
taking all the terms from LHS to RHS:
=> 0 = x² - 4x -2x + 5x + 15
solving the like terms together:
=> 0 = x² - x + 15 . . . . .(¡¡¡)
that's the standard form!
comparing it with eqn. (¡)
we get,
[If the display of the answer isn't clear, check the attachment]