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Roots of Quadratic Equation

What should b...

Question

What should be added to $1 + 2 x - 3 x^{2}$ to get $x^{2} - x - 1$ ?

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Solution

According to the problem,
Let A should be added to $1 + 2 x - 3 x^{2}$ to get result,

$\begin{matrix} 1 + 2 x - 3 x^{2} + A = x^{2} - x - 1 A = x^{2} - x - 1 - (1 + 2 x - 3 x^{2}) A = x^{2} - x - 1 - 1 - 2 x + 3 x^{2} A = 4 x^{2} - 3 x - 2 \end{matrix}$
Therefore, $4 x^{2} - 3 x - 2$ added to the equation.

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