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Use the value of the discriminant to determine the number and type of roots for each equation.X^2=4x-4

Use the value of the discriminant to determine the number and type of roots for each-example-1
User Brian Hawk
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The first step we have to follow is to write the equation in standard form:


\begin{gathered} x{}^2=4x-4 \\ x^2-4x+4=0 \end{gathered}

The discriminant of a quadratic expression is given by:


D=b^2-4ac

If the discriminant is greater than 0 and has a rational square root, the equation has 2 real rational roots; if it is greater than 0 and does not have a rational square root, the equation has 2 real irrational roots; if it is equal to 0, the equation only has 1 real rational root; and if it is less than 0, the equation has no real roots.

Find the discriminant using the values of the equation:


\begin{gathered} D=(-4)^2-4(1)(4) \\ D=16-16 \\ D=0 \end{gathered}

It means that this equation has 1 real, rational root.

User Marcus Henrique
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