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The equation 2x^2 + 2kx + (k + 2) = 0, where k is a constant, has two distinct real roots. Show that k satisfies k^2 – 2k – 4 > 0

Two distinct real roots means that we can use b^2-4ac>0 relationship for any ax^2+bx+c equation. Apply the above gives, 4k^2 - 4 2 (k+2)>0 Simplifying gives, k^2 - 2k -4 >0
AT
Answered by Andreas T. • Maths tutor
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How to find and classify stationary points (maximum point, minimum point or turning points) of curve.

To find the stationary points of a function we must first differentiate the function. The derivative tells us what the gradient of the function is at a given point along the curve. Therefore, should we find ...
CJ
Answered by Callum J. • Maths tutor
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Find the equation of the tangent to the curve y = (2x -3)^3 at the point (1, - 1), giving your answer in the form y = mx + c.

y = (2x -3)^3 y = (2x)^3 + 3.((2x)^2)(-3) + 3.(2x).(-3)^2 + (-3)^2 using Pascal's Triangle. y = 8x^3 - 36x^2 + 54x - 27 dy/dx = 24x^2 - 72x + 54 at point (1,-1); dy/dx = 24 -72 + 54 = 6 Therefore tangent lin...
RS
Answered by Robert S. • Maths tutor
13239 Views

Find the first derivative of y=2^x

There is an initial subtle difficulty to this question, and it highlights understanding of the relationship between natural logarithms and the exponential function. One of the ways to solve this question, is...
AM
Answered by Alex M. • Maths tutor
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What is Pythagoras' Theorem and how do you use it?

Pythagoras' Theorem: a 2 + b 2 = c 2 where a, b, c relate to the sides of a right-angled triangle, and c is the hypoteneuse. Use the equation to find the length one side if you only know the lengths of two o...
HS
Answered by Hermione S. • Maths tutor
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