4. Procedure for solving quadratic equations through intersection of lines

If \(2\) quadratic equations were provided, we need to determine the point of intersection of these two lines.

 

The steps to find the roots of the intersection point of a quadratic equation are given by:

 

Step 1: Draw the graph of the quadratic equation, we get a parabola.

 

Step 2: Now, subtract the \(2\) quadratic equations, and we get an equation of a straight line.

 

Step 3: Draw the graph of the straight line.

 

Step 4: (i) If the straight line intersects the parabola at \(2\) distinct points, then the \(x\) - coordinates of the point of intersection will be the roots of the given quadratic equation.

 

(ii) If the straight line intersects the parabola at only \(1\) point, then the \(x\) - coordinate of the point of intersection will be the root of the given quadratic equation.

 

(iii) If the straight line does not intersect the parabola, then the given quadratic equation will have no real roots.