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The equation (t – 1)x^2 + 4x + (t – 5) = 0, where t is a constant has no real roots. Show that t satisfies t2–6t+1>0

This is a quadratic equation of the form ax^2 + bx +c, where (t-1)=a 4=b . (t-5)=0 Therefore if there are no real roots, you get that b^2-4ac<0. (using the quadratic formula) First plug in values for a b ...
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Answered by Rachel Y. • Maths tutor
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What is negative feedback in terms of homeostasis?

To regulate a number of processes in the body, there needs to first be recognition of current levels in order to respond in the appropriate way. For example there is a temperature "norm" (~36.9°C),...
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Answered by Charlotte D. • Biology tutor
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What is homeostasis?

This is the way that the body maintains a stable internal environment, which is vital for correct functioning of the cells in the body. For a stable environment there are several things which need to be regu...
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Answered by Charlotte D. • Biology tutor
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Explain metallic bonding

Metallic bonding occurs due to electrostatic forces of attraction between a lattice of positively charged ions and a "sea" of delocalised electrons. (Draw diagram) These electrostatic forces are ve...
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Answered by Nikhita G. • Chemistry tutor
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Question 3 on the OCR MEI C3 June 2015 paper. Find the exact value of Integral x^3 ln x dx between 1 and 2.

This is a good candidate for integration by parts because it is a product of two functions – ln(x) and x^3, and x^3 is easy to integrate. The definition for integration by parts is: integral(u dv/dx) dx = uv...
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Answered by Tom K. • Maths tutor
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