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How do I know how many solutions a quadratic equation has?

A quadratic equation is an equation that looks like: x 2 + 4x - 2 = 0. The general form of this is written as ax 2 + bx + c = 0, where a, b and c are all numbers, and x is our unknown variable. In the exampl...
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Answered by Nathan C. Maths tutor
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Why does the First Ionisation Energy decrease down a group in the Periodic Table?

Two major factors control how tightly held the outermost electron is and therefore how much energy is required to remove it, which gives us the size of the Ionisation energy. The first of these factors is sh...
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Answered by Daniel K. Chemistry tutor
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What is meant by the 'First Ionisation Energy' of an element?

The ionisation energy of an element is the energy required to remove the one of the outermost electrons from an atom of the element in its gaseous state. This is quite a difficult process to measure the ener...
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Answered by Daniel K. Chemistry tutor
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What is the best approach to analysing an extract?

A listening exam is daunting. There is not a lot of time to analyse an extract, so you need to find the quickest and most efficient way to gain marks. There are many different ways to approach an extract, an...
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To differentiate a simple equation: y= 4x^3 + 7x

y = 4x^3 + 7 x Recall: to differentiate any function of the form y = x^n dy/dx = y' = n x^(n-1) Hence if y = 4x^3 + 7x dy/dx = 4 ( 3x^3 -1) + 7x^(1-1) = 12 x^2 + 7
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