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If x is a real number, what are the solutions to the quadratic: 4*x^2- 4*x+1 = 0

You first calculate the delta of the equation: delta = b^2-4 a c = 16 - 16 = 0 => the solution is double.x1,2 = (-b±sqrt(delta))/2/a = 4/2/4 = 1/2 which is real.so the solutions are 1/2 and 1/2.
MI
Answered by Maria I. • Maths tutor
3686 Views

How to solve the following for x: (2x+3)/(x-4) - (2x-8)(2x+1) = 1

(The full answer produced answer is annotated working out, but since this text box won't let me submit pictures, I'll do my best to transcribe)First, we gather the two fractions by using a common denominator...
CF
Answered by Cal F. • Maths tutor
3848 Views

The equation x^2+ kx + 8 = k has no real solutions for x. Show that k satisfies k^2 + 4k < 32.

If a quadractic equation ax^2 + bx + c = 0 has no real solutions, this means that the discriminant is less than 0, i.e. b^2-4ac&lt;0. Let's put our equation in this form: x^2 + kx + 8 = k rearranges to x^2 +...
TD
Answered by Tutor91955 D. • Maths tutor
15959 Views

Find the equation of the tangent to the curve y^3 - 4x^2 - 3xy + 25 = 0 at the point (2,-3).

This is an example of implicit differentiation where we have to consider both the y-terms as well as the x-terms. The first step is to deal with each term on the left hand side individually. This gives us 3y...
TJ
Answered by Tanmayi J. • Maths tutor
5127 Views

Joan cycles from her house to a shop 900 m away. She then cycles to her friends' house 700 m away. The average speed for the first part of her journey is 2 m/s. The second part takes her 16 mins. What is the average speed for her entire journey?

S: 900 700D: 2 m/sT: 960s Need to find speed in seconds so convert 16 mins to seconds. To find average, we must find time for the first part. Using the basic D/S, the time is 900/2 = 450 s.Speed for the seco...
AR
Answered by Aisha R. • Maths tutor
3339 Views