Determine for what values of c, f(x)=4x^2-(2c+8)x+4 has no real roots.
For f(x) not to have any real roots, its discriminant, b2-4ac < 0. Plugging in the coefficients from f(x), this means (-(2c+8))2-4x4x4 < 0.This means (-(2c+8))2 < 4x4x4So 4c2+32c+64 < 64 by multiplying out the brackets.This means 4c2+32c < 0So c2+8c < 0, which factorised gives c(c+8) < 0As this has roots at c=-8 and c=0, by plotting a graph we can see that the range of values of -8<x<0.
AR
Related Maths Scottish Highers answers
All answers ▸a) Factorise: 2x^2-72, and hence b) find the y-intercept of the line with the equation: y=(2x^2-72)/(4x-24)
The equation x^2 + (k-5)x + 1 = 0 has equal roots. Determine the possible values of k.
Solve algebraically the system of equations: 4x+5y=-3 and 6x-2y=5
A triangle has vertices A(-3,5), B(7,9) and C(2,11). What is the equation of the median that passes through the vertex C?