What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?

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26-05-2018
Mathematics

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What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?

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gmany gmany · Answer 1 · 2018-05-31T14:53:38+02:00

[tex]2x^2+16x-9=0\ \ \ |+9\\\\2x^2+16x=9\ \ \ |:2\\\\x^2+8x=4.5\\\\x^2+2x\cdot4=4.5\ \ \ |+4^2\\\\\underbrace{x^2+2x\cdot4+4^2}_{(a+b)^2=a^2+2ab+b^2}=4.5+4^2\\\\(x+4)^2=20.5\to x+4=\pm\sqrt{20.5}\\\\x+4=-\sqrt{\dfrac{205}{10}}\ \vee\ x+4=\sqrt{\dfrac{205}{10}}\\\\x+4=-\sqrt{\dfrac{2050}{100}}\ \vee\ x+4=\sqrt{\dfrac{2050}{10}}\\\\x+4=-\dfrac{\sqrt{25\cdot82}}{10}\ \vee\ x+4=\dfrac{\sqrt{25\cdot82}}{10}\\\\x=\dfrac{-40-5\sqrt{82}}{10}\ \vee\ x=\dfrac{-40+5\sqrt{82}}{10}[/tex]