Dick said:That's just an equation. What's the actual problem? Are you supposed to find A, B, and C given the equation is true for all x? That's just a guess.
Borek said:A(x-1)2 + Bx + C = Ax2 + (B-2A)x + A+C
So at least A=2 is obviously OK, then A+C=2+C=-5, so C=-7. B-2A=B-4=7, so B is OK too.
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The purpose of solving quadratic identities is to find the values of the unknown variables (A, B, and C) in the equation that satisfies the given conditions. This helps in understanding the behavior and properties of quadratic equations and can be used to solve real-world problems.
To solve quadratic identities, the first step is to simplify the equation using algebraic techniques such as factoring or the quadratic formula. Then, equate the coefficients of each term to the corresponding terms on the other side of the equation. Finally, solve the resulting system of equations to find the values of A, B, and C.
A quadratic identity is an equation that is always true for any value of the variable, while a quadratic equation has a specific solution for the variable. In other words, a quadratic identity is an equation that is true for all values of x, whereas a quadratic equation has a finite set of solutions.
Yes, quadratic identities can have complex solutions. This occurs when the discriminant (b^2-4ac) is negative, resulting in complex roots. Complex solutions are represented in the form of a+bi, where a and b are real numbers and i is the imaginary unit.
Quadratic identities have various applications in real life, such as in physics, engineering, economics, and computer graphics. They can be used to model and analyze physical phenomena, optimize systems, predict trends in data, and create computer-generated images.