FINDING NATURE OF ROOTS OF QUADRATIC EQUATION BY GRAPHING

To obtain the roots of the quadratic equation in the form ax² + bx + c = 0 graphically, first we have to draw the graph of y = ax² + bx + c .

The solutions of the quadratic equation are the x coordinates of the points of intersection of the curve with X axis.

Finding the Nature of Roots of Quadratic Equations Graphically

Solved Questions 

Question 1 :

Graph the following quadratic equations and state their nature of solutions.

x² + x + 7  =  0

Solution :

Draw the graph for the function y = x² + x + 7

Let us give some random values of x and find the values of y.

Points to be plotted :

(-4, 19) (-3, 13) (-2, 9) (-1, 7) (0, 7) (1, 9) (2, 13) (3, 19) (4, 27)

To find the x-coordinate of the vertex of the parabola, we may use the formula x = -b/2a

x = -1/2(1)  =  -1/2

By applying x = -1/2, we get the value of y.

y = (-1/2)² + (-1/2) + 7 

y = (1/4) - (1/2) + 7

y = (1 - 2 + 28)/4  =  27/4

Vertex (1/2, 27/4)

The graph of the given parabola does not intersect the x-axis at any point. Hence it has no real roots.

Question 2 :

Graph the following quadratic equations and state their nature of solutions.

x² − 9  =  0

Solution :

Let us give some random values of x and find the values of y.

Points to be plotted :

(-4, 7) (-3, 0) (-2, -5) (-1, -8) (0, -9) (1, -8) (2, -5) (3, 0) (4, 7)

To find the x-coordinate of the vertex of the parabola, we may use the formula x = -b/2a

x = 0/2(1)  =  0

By applying x = 0, we get the value of y.

y = 0² - 9

y = -9

Vertex (0, -9)

The graph of the given parabola intersects the x-axis at two points. Hence it has two real and unequal roots.

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