Roots ofQuadratic Equations
A quadratic equation is a polynomial whichhas a degree of two which means that the maximum power of thevariable in the equation is 2. A quadratic eqtn is in represented as:ax2 + bx +c =0. Here a cannot be equal to zero becausethen it will change into linear equation.
Roots ofQuadratic Equations mean the two values of the variablethat will satisfy the equation. the two values can be same in somecases but they will be opposite in sign or same in magnitude andsign. Graphically Roots of the QuadraticEquation represents the points on which the graph ofequation (which is a parabola) cuts the axes.
As shown in graphsgiven below the roots of first quadratic equation are -1 and 3 while thatof second equation are 0 and 4. If the equation is in x variable thenits roots will lie on x axis while if the equation is in y then rootswill lie on y axis.
If p and q are roots of the equationax2 + bx +c =0, then x-p and x-q will be the factors ofthe quadratic eqn which means that ax2 + bx +c = (x - p)(x - q).
A quadratic eqn can have differenttypes of roots depending on the value of a term ‘D’ or which isgiven as: D="b2 – 4ac. Let us see the conditions:
If D>0 then the equation willhave two real and unequal roots.
If D="0" then the equation will havereal and equal roots = -b/2a.
If D<0 then he equation willhave imaginary roots.
Unequal real roots mean that the graphof equation will cut the axis at two points while equal roots meanthat it touch the axis at one point: