Quadratic 83667

A quadratic equation is given: x²-x-2=0

Without solving this equation, construct a quadratic equation whose roots are the square of the roots of the given equation.

Correct answer:

y₁ =  4
y₂ =  1

Step-by-step explanation:

$$\begin{gathered} x^2-x-2=0 \\ {x}^2-x-2=0 \\ a=1;b=-1;c=-2 \\ D=b^2-4ac=1^2-4\cdot 1\cdot (-2)=9 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{1\pm \sqrt{9}}{2} \\ {x}_{1,2}=\frac{1\pm 3}{2} \\ {x}_{1,2}=0.5\pm 1.5 \\ {x}_1=2 \\ {x}_2=-1 \\ {y}_1=x_1^2=2^2=4 \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} y_2=x_2^2=(-1{)}^2=1 \\ (y-y_1)\cdot (y-y_2)=0 \\ (y-1)\cdot (y-4)=0 \\ {y}^2-5y+4=0 \end{gathered}$$

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