what does it mean if "b^2 - 4ac < 0" for a quadratic equation (eg y = a*x^2 + b*x + c)
The question comes from the quadratic equation r = (-b +- sqrt(b2 - 4ac)/2a where r is the root or x coordinate where the line crosses the x-axsis (the y coordinate is always 0). If b2 - 4ac < 0 then to find the root you whoud have to take the sqrt of a negative number which doesnt exsist (at least it doesn't for standard maths alevel students) and so the line doesnt have any roots. This means that it doesnt cross the x-axsis.
NW
Related Maths A Level answers
All answers ▸Find the coordinates of the turning points of the curve y = 4/3 x^3 + 3x^2-4x+1
Find all solution to the equation 3tan(x)=8/sin(x) for 0<=x<=360 degrees
Find the stationary points and their nature of the curve y = 3x^3 - 7x + 2x^-1
AQA PC4 2015 Q5 // A) Find the gradient at P. B) Find the equation of the normal to the curve at P C)The normal P intersects at the curve again at the point Q(cos2q, sin q) Hence find the x-coordinate of Q.