When is factorisation most effective?
Factorisation works best when the quadratic equation can be split into integer factors easily.
What is the factorisation method?
Factorisation rewrites a quadratic equation as a product of two linear factors to find the variable's value
Where are quadratic equations used?
Quadratic equations are used in physics, geometry, economics, engineering, and optimization problems.
What determines the nature of roots?
The discriminant Δ = b²-4ac determines if roots are real, repeated, or complex.
What is the quadratic formula?
x = (-b+-√b²-4ac) / 2a
What are the methods to solve quadratic equations?
Factorization, completing the square, quadratic formula, and graphical method.
What is a quadratic equation?
A polynomial equation of degree two is expressed as ax² + bx + c, where a≠0.
What if the system of equations has no solution or infinitely many solutions?
If the equations represent parallel lines, there is no solution. If they represent the same line, there are infinitely many solutions. This can be determined by comparing the ratios of the coefficients.
How can I verify the solution obtained from these methods?
Substitute the obtained values of x and y back into the original equations to ensure both equations are satisfied.
Are there scenarios where the elimination method is more efficient than the substitution method?
Yes, the elimination method is more efficient when the coefficients of one variable are already aligned or can be easily manipulated to align, allowing for quick elimination.
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