Question

Draw the graph of ax² + bx +C =0(a is not equal to 0) having distinct roots.​

Answer 1

Step-by-step explanation:

which vertex is (-b/2a, -D/4a). where D is discriminant.i.e., D = b² - 4ac.

there are three situations possible for quadratic equation

when D = b² - 4ac = 0 , it means quadratic touch at a point on x-axis. hence, roots of quadratic equation will be equal.

when D = b² - 4ac < 0, it means quadratic equation doesn't have real roots. because it neither touches nor intersects the x-axis.

when D = b² - 4ac > 0, it means quadratic equation have real roots and both are distinct. graph of quadratic equation intersects two two points on the x-axis.

here we have to draw the last situation (situation no 3). vertex = (-b/2a, D/4a)

and roots are α and β

so, graph would be as shown in figure.