- #1
Sumedh
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Homework Statement
If 3x2+2αxy+2y2+2ax-4y+1 can be resolved into two linear factors, prove that α is the root of the equation x2+ 4ax+2a2+6=0.
please don't solve the problem
just hint is expected.
Sumedh said:please don't solve the problem
just hint is expected.
Sumedh said:then what about 3x2 and 2ax
Sumedh said:after arranging the original eq. with respect to x
i got this (...)x2 +(...)x+c
by finding its discriminant and equating it to zero
on solving i got
...etc...
after equating what should i do?
A quadratic equation with two variables is an algebraic expression that contains two variables, typically represented as x and y, and involves terms with exponents of 2. An example of a quadratic equation with two variables is x2 + 2xy + y2 = 25.
The main problem in solving a quadratic equation with two variables is that there are infinitely many solutions. This is because there are two variables, and for every value of one variable, there can be multiple values of the other variable that satisfy the equation. Therefore, it is not possible to find a single solution for a quadratic equation with two variables.
To graph a quadratic equation with two variables, you can use a coordinate plane and plot points that satisfy the equation. Since there are infinitely many solutions, it is not possible to draw a single line or curve to represent the entire equation. Instead, you can plot several points and connect them to get a general idea of the shape of the equation.
Yes, a quadratic equation with two variables can have negative solutions. This is because the values of the two variables can be positive, negative, or zero. However, it is not possible to have a negative value for both variables at the same time, as this would result in a negative number squared, which is not possible.
Quadratic equations with two variables are commonly used in physics and engineering to model and solve problems involving motion, such as projectile motion and free fall. They are also used in economics to study demand and supply, and in biology to analyze population growth. Additionally, they can be used in optimization problems, such as finding the maximum or minimum value of a function.