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How many distinct real roots does the equation x^3 − 30x^2 + 108x − 104 = 0 have?

We can see that 104 = 2^3 * 13 = 2 2 26, 30 = 2 + 2 + 26, and 108 = 2 2 + 2 26 + 2*26, so the coefficients agree with the Vieta's formulas, so the roots of the equation above are 2, 2, 26. In conclusion, it ...
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Answered by Andreea I. • MAT tutor
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The quadratic equation 2x^2 + 8x + 1 = 0 has roots a and b. Write down the value of a + b, a*b and a^2 + b^2.

Using Vieta's formulas, which make the correspondence between the sums and products of the roots of a polynomial and its coefficients, we can deduce that a + b = (-8)/2 = -4, a b = 1/2 =0.5 and a^2 + b^2 = (...
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Answered by Andreea I. • Maths tutor
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What is a geometric series?

A geometric series is a series with a constant ratio between successive terms.
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Answered by Ming Fung Y. • Maths tutor
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What is an Inverse function?

An inverse function is a function that "reverses" another function. That is, if f is a function mapping x to y , then the inverse function of f maps y back to x . [1]
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Answered by Ming Fung Y. • Maths tutor
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How does filtration through the kidney work?

There are 3 key stages in filtration through the Kidney: Firstly, blood is pushed through a tubular structure called the glomerulus - imagine a bowl of noodles. The pressure of the blood in the glomerulus ca...
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Answered by Alastair P. • Biology tutor
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