Derive the Quadratic Equation Find the Quadratic Equation whose roots are $2+\sqrt3$ and $2-\sqrt3$.
Some basics:


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*The general form of a Quadratic Equation is $ax^2+bx+c=0$


*In Quadratic Equation, $ax^2+bx+c=0$, if $\alpha$ and $\beta$ are the roots of the given Quadratic Equation, Then,
$$\alpha+\beta=\frac{-b}{a}, \alpha\beta=\frac{c}{a}$$

I am here confused that how we can derive a Quadratic Equations from the given roots

Here $$-\frac ba=\alpha+\beta=2+\sqrt3+2-\sqrt3=4$$ and
$$\frac ca=\alpha\beta=(2+\sqrt3)(2-\sqrt3)=2^2-3=1$$
So, the quadratic equation becomes $$x^2-4x+1=0$$
