Overview
these are my classmates discussions that we need to leave a comment 3-4 sentences. 1) The relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses is that if the discriminant value is greater than 0, this would mean that the equation has two real roots that are different in value. In addition, if the discriminant is less than 0, it has no real roots; if the discriminant value is equal to 0, it has two identical roots.
The position of the roots of the polynomials on its graph with its discriminant and the sign of the discriminant is that if the discriminant is greater than zero(positive number), it will intersect twice at the x-coordinate. If it is less than zero(negative number), it does not intersect the x-intersect; if it is equal to zero, it intersects once at the x-coordinate. 2) After doing some research, the value of the discriminant shows us how many roots the polynomial possesses. If the discriminant b2 - 4ac is greater than zero, then the quadratic function has two distinct real roots. On a graph, it will cross the x axis twice. If b2 - 4ac is equal to zero, then the quadratic function has one repeated real root and will touch the x axis. If b2 - 4ac is less than zero, then the quadratic function has no real roots and will not touch the x axis.
Here is an example, let's say we are given this problem:
Determine the discriminant value and the nature of the roots for the given quadratic equation 3x2+2x+5.
Based on the quadratic equation, we know that A=3, B=2 and C=5.
When we plug these numbers into b2 - 4ac, we get (2)2 - 4(3)(5).
Our discriminant value ends up being -56. -56 is less than zero therefore it has no real roots and will not touch the x axis.