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The equation (k+3)x^2 + 6x + k =5 has two distinct real solutions for x. Prove that k^2-2k-24<0

We argue using the discriminant of a quadratic polynomial. For a quadratic ax^2 + bx + c=0, the discriminant D is D = b^2 - 4ac. When this quadratic has two distinct real roots, we have that D &gt; 0. So we ...
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Answered by Huw D. • Maths tutor
16337 Views

I don't understand why the function "f(x)=x^2 for all real values of x" has no inverse. Isn't sqrt(x) the inverse?

I don't understand why the function &quot;f(x)=x^2 for all real values of x&quot; has no inverse. Isn't sqrt(x) the inverse? I like to think of a function a bit like a machine. It takes in a number, and turn...
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Answered by Benjamin M. • Maths tutor
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What is the central dogma of molecular biology?

It explains the flow of information in biological systems, especially in eukaryotes. It can be simplified to &quot;DNA makes RNA makes protein&quot;. This explains how DNA, which is passed down the generatio...
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Answered by Kalyan M. • Biology tutor
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To what extent was government transformed during the reign of Henry VIII?

During the reign of Henry VIII there was broad structural change in central governance brought about by the transformative effects of the Reformation, and there was a fundamental shift in the structure of au...
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Answered by Mimi T. • History tutor
32228 Views

What is the difference between transcription and translation?

This is a rather fundamental question and it's important to get it right. Remember, the central dogma of biology is, in its most basic form, DNA makes RNA makes protein. Transcription is the process by which...
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Answered by Serena M. • Biology tutor
6881 Views