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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 = 2226, 30 = 2 + 2 + 26, and 108 = 22 + 226 + 2*26, so the coefficients agree with the Vieta's formulas, so the roots of the equation above are 2, 2, 26...

AI
Answered by Andreea I. MAT tutor
9984 Views

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, ab = 1/2 =0.5 and a^2 ...

AI
Answered by Andreea I. Maths tutor
6253 Views

What is a geometric series?

geometric series is a series with a constant ratio between successive terms.

MF
Answered by Ming Fung Y. Maths tutor
4648 Views

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...

MF
Answered by Ming Fung Y. Maths tutor
5165 Views

How does filtration through the kidney work?

There are 3 key stages in filtration through the Kidney:

  1. Firstly, blood is pushed through a tubular structure called the glomerulus - imagine a bowl of noodle...
AP
Answered by Alastair P. Biology tutor
3793 Views

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