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anemone
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Find the product of real roots of the equation ##x^2+18x+30=2\sqrt{x^2+18x+45}##.
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My best guess is that x2 was indeed meant to represent ##x^2##.malawi_glenn said:is x2 = ##x^2##?
Find the product of real roots of the equation x^2+18x+30=2x^22+18x+45.
I would say that the equation has no real roots hence the product of real roots is not defined.
Unless I have missed something REALLY obvious or some technicality.
Hello again to all!anemone said:Find the product of real roots of the equation ##x^2+18x+30=2\sqrt{x^2+18x+45}##.
Yes, that's more like it!anemone said:I hope this problem looks more interesting to you now!
The POTW equation is a mathematical equation that represents a polynomial with real coefficients. It stands for "Product of the Two Roots of a Polynomial".
To solve the POTW equation, you need to first find the roots of the polynomial. This can be done by factoring the polynomial or by using the quadratic formula. Once you have the roots, simply multiply them together to find the product.
Finding the product of real roots is important because it gives us information about the behavior of the polynomial. The product of the roots can tell us whether the polynomial has a positive or negative leading coefficient, and whether the graph of the polynomial will have a positive or negative end behavior.
No, the POTW equation can only be used for polynomials with real roots. Complex roots cannot be multiplied together to find a product.
Yes, there are other methods such as using the Vieta's formulas or the Descartes' rule of signs. However, these methods are more complex and are not as commonly used as factoring or the quadratic formula.