2x2 - 5x - 3 = 0
A quadratic equation expressed in the form ax2 + bx + c = 0 has two real and distinct roots when b2 - 4ac is positive.
Using the figures from the supplied equation then b2 - 4ac = 52 - (4 x 2 x -3) = 25 + 24 = 49.
Therefore there are TWO real and distinct roots.
Chat with our AI personalities
It has two complex roots.
A cubic has from 1 to 3 real solutions. The fact that every cubic equation with real coefficients has at least 1 real solution comes from the intermediate value theorem. The discriminant of the equation tells you how many roots there are.
There are infinitely many answers and they comprise the coordinates of all points on the line that satisfy the equation.
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
It has the following solutions.