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Express
[tex]2x {}^{2} - 20x + 53[/tex]
In the form
[tex]2(x - p) {}^{2} + q[/tex]
Where p and q are integers.

The answer to this is
[tex]2(x - 5) {}^{2} + 3[/tex]
Use this result to explain why the equation
[tex]2x {}^{2} - 20x + 53 = 0[/tex]
has no real roots



Respuesta :

gmany
[tex]ax^2+bx+c=a(x-p)^2+q\ where\\\\p=\dfrac{-b}{2a};\ q=f(p)=\dfrac{-(b^2-4ac)}{4a}[/tex]
We have:
[tex]2x^2-20x+53\to a=2;\ b=-20;\ c=53[/tex]
substitute
[tex]p=\dfrac{-(-20)}{2\cdot2}=\dfrac{20}{4}=5\\\\q=f(5)=2\cdot5^2-20\cdot5+53=2\cdot25-100+53=50-100+53=3[/tex]
therefore we have the answer:
[tex]2x^2-20x+53=2(x-5)^2+3[/tex]

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