Consider the equation 2x2-3x plus k equals 0for what values of m is one root double the other root?
2x2 - 3x + k = 0
a = 2, b = -3, c = k
D = b2 - 4ac = (-3)2 - 4(2)(k) = 9 - 8k
D = 0 gives us a double root.
9 - 8k = 0 add 8k to both sides
9 = 8k divide by 8 to both sides
9/8 = k
Thus for k = 9/8 we have a double root, which is x = -b/2a. So that x = -(-3)/2(2) = 3/4.
Find an equation of variation where y varies directly as x One pair of values is y equals 80 when x equals 40?
It's a single linear equation in two variables. The graph of the equation is a straight line; every point on the line is a set of values that satisfy the equation. In other words, there are an infinite number of pairs of (x,y) values that satisfy it. In order to figure out numerical values for 'x' and 'y', you would need another equation.
Where are the points of intersection of the straight line 3x -y equals 5 with the curve 2x squared plus y squared equals 129?
This is a quadratic equation requiring the values of x to be found. Rearrange the equation in the form of: -3x2-4x+6 = 0 Use the quadratic equation formula to factorise the equation: (-3x+2.69041576)(x+2.23013857) Therefore the values of x are 0.8968052533 or - 2.230138587 An even more accurate answer can be found by using surds instead of decimals.
This is a simultaneous equation question. 4x-4y = -40 4x+43 = y Rearrange the second equation so that all the letters and numbers are in line with the first equation remembering to alter the values of the + and - signs. 4x-4y = -40 4x-y = -43 Subtract the second equation from the first equation remembering that a - - is equal to a + This will leave you with -3y = 3 and by…