Answer:
Step-by-step explanation: When the left side factors into two linear equations with the same solution, the quadratic equation is said to have a repeated solution. We also call this solution a root of multiplicity 2, or a double root.
Double roots of a quadratic equation shows that they are same root, and the graph of the quadratic function merely touches the input axis.
Let there is a quadratic function as: [tex]y = ax^2 + bx + c[/tex]
The input axis is 'x-axis' and the output axis is 'y-axis'
When the output is 0, we get the graph of that function touching the x-axis since the place where y is 0 is only x-axis.
Thus, putting [tex]ax^2 + bx +c = 0[/tex] gives us the values of x for which the graph of the function [tex]y = ax^2 + bx + c[/tex] intersects the x-axis.
These points of interesection are called roots of the quadratic equation.
If the graph only touches the input axis (here x-axis), then both the roots are lying on same point and therefore are of equal measurement.
This is the condition when we call that the considered quadratic equation has double roots.
Let we consider and example of a quadratic function which will have double root.
Since (x-3)(x-3) = 0 will give x= 3 two times, that means the roots of the equation (x-3)(x-3) are same, and are equal to 3.
So, [tex]y = (x-3)(x-3) = x^2 -6x +9[/tex] is one such quadratic function having double roots, as shown in the image attached below.
Learn more about finding the nature of the roots of a quadratic equation here:
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