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Show that x^2 - 8x +17 <0 for all real values of x

consider the discriminant b2-4ac 82-4x1x17 64-68=-4 discriminant is below 0, there are no real roots therefore x2 - 8x +17 <0

Answered by Maths tutor
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Solve x^2 + 12 = 6 - 5x by factorisation.

This question is best answered by breaking the process down into a number of smaller steps.Step 1: Rearrange the equation so that both sides are equal to 0 (in other words, add and subtract terms ...

Answered by Yipeng C. Maths tutor
2494 Views

Calculate the first derivative of f( x)= 3x^3+2x^2-5

f’(x)= 9x^3+4x

Answered by Maths tutor
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The point P has coordinates (4, 5). The point Q has coordinates (a, b). A line perpendicular to PQ is given by the equation 5x+3y=11. Find an expression for b in terms of a.

First we should find the gradient of the line perpendicular to PQ by rearranging the equation.5x+3y=113y=11-5xy=11/5 -5/3xy= -5/3x + 11gradient is -5/3.We know that the gradients of perpendicular lines mu...

Answered by Staś B. Maths tutor
3359 Views

Let f(x) = 3x^4 - 8x^3 - 3. Find the x- values of the stationary points of this function.

Stationary points occur when f'(x) = 0. To find this, we differentiate f(x) to get f'(x) = 12x^3 - 24x^2. We know that at the stationary points are when f'(x) = 0. so we know that 12x^3 - 24x^2 = 0. We ca...

Answered by Yathavan S. Maths tutor
2711 Views

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