how many methods to solve quadratic equation explain in brief
Answers
Answer:
factorization
completing square method
quadratic formula
graphic
Answer:four methods
The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.
Step-by-step explanation:
Solve for x in the following equation.
Example 1: text2html_wrap_inline253 tex2html_wrap_inline321
The equation is already set to zero.
Method 1:text2html_wrap_inline253 Factoring
eqnarray60
eqnarray64
Method 2:text2html_wrap_inline253 Completing the square
Divide both sides of the equation tex2html_wrap_inline323 by 2.
eqnarray80
Add tex2html_wrap_inline325 to both sides of the equation.
eqnarray97
Add tex2html_wrap_inline327 to both sides of the equation:
eqnarray121
Factor the left side and simplify the right side :
eqnarray133
Take the square root of both sides of the equation :
eqnarray141
Add tex2html_wrap_inline329 to both sides of the equation :
eqnarray150
Method 3:text2html_wrap_inline253 Quadratic Formula
The quadratic formula is tex2html_wrap_inline331
In the equation tex2html_wrap_inline333 ,a is the coefficient of the tex2html_wrap_inline335 term, b is the coefficient of the x term, and c is the constant. Substitute 2 for a, -1 for b, and -1 for c in the quadratic formula and simplify.
eqnarray189
eqnarray196
Method 4:text2html_wrap_inline253 Graphing
Graph y= the left side of the equation or tex2html_wrap_inline341 and graph y= the right side of the equation or y=0. The graph of y=0 is nothing more than the x-axis. So what you will be looking for is where the graph of tex2html_wrap_inline341 crosses the x-axis. Another way of saying this is that the x-intercepts are the solutions to this equation.
You can see from the graph that there are two x-intercepts, one at 1 and one at tex2html_wrap_inline353 .
The answers are 1 and tex2html_wrap_inline357 These answers may or may not be solutions to the original equations. You must verify that these answers are solutions.
Check these answers in the original equation.
Check the solution x=1 by substituting 1 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.
Left Side: tex2html_wrap_inline367
Right Side: tex2html_wrap_inline369
Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 1 for x, then x=1 is a solution.
Check the solution tex2html_wrap_inline373 by substituting tex2html_wrap_inline353 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.
Left Side: tex2html_wrap_inline377
Right Side: tex2html_wrap_inline369
Since the left side of the original equation is equal to the right side of the original equation after we substitute the value tex2html_wrap_inline353 for x, then tex2html_wrap_inline373 is a solution.
The solutions to the equation tex2html_wrap_inline385 are 1 and tex2html_wrap_inline389