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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
12922 Views

How does the mechanism for electrophilic addition work?

First we must consider what an elecrophile is. An electrophile is a molecule or ion which is attracted to (and accepts electrons from) electron dense regions in other molecules, because it is positively char...
AR
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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
19213 Views

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
13241 Views

How do I prepare for and write an essay on an unseen poem?

The best preparation for essays on unseen poems is knowing a list of key literary devices and themes that you should be on the lookout for as you get to know the poem in front of you. Because you won't have ...
TD
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