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What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$?

 

f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

 

Your answer should be a list of numbers and should not include variable names, nor should it include $y$-coordinates.

 Feb 18, 2025
 #1
avatar+15054 
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\(f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.\\ f(x)=-3x^2+3x+27\\ x^2-x-9=0\\ x_0\in \{\frac{1}{2}\pm \sqrt{(\frac{1}{2})^2+9}\}\\ x_0\in \{\frac{1}{2}+\sqrt{9.25},\frac{1}{2}-\sqrt{9.25}\}\\ \color{blue}x_0\in \{3.541, -2.541\}\)

 

The x-coordinate(s) of all point(s) where the parabola y = f(x) intersects the line y = 0

are \(\color{blue}x_0\in \{3.541, -2.541\}.\)

 

laugh !

 Feb 19, 2025

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