(i) x^2 + x + 7 = 0 (ii) x^2 – 9 = 0

Question

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

(i) x² + x + 7 = 0

(ii) x² – 9 = 0

Answer 1

(i) Let y = x² + x + 7

Step 1:

Step 2: Points to be plotted: (-4, 19), (-3, 13), (-2, 9), (-1, 7), (0, 7), (1, 9), (2, 13), (3, 19), (4, 27) 

Step 3: Draw the parabola and mark the co-ordinates of the parabola which intersect with the x-axis.

Step 4: The roots of the equation are the points of intersection of the parabola with the x axis. Here the parabola does not intersect the x axis at any point.

So, we conclude that there is no real roots for the given quadratic equation.

(ii) Let y = x² – 9 

Step 1:

Step 2: The points to be plotted: (-4, 7), (-3, 0), (-2, -5), (-1, -8), (0, -9), (1,-8), (2, -5), (3, 0), (4, 7) 

Step 3: Draw the parabola and mark the co-ordinates of the parabola which intersect the x-axis.

Step 4: The roots of the equation are the co-ordinates of the intersecting points (-3, 0) and (3, 0) of the parabola with the x-axis which are -3 and 3 respectively. 

Step 5: Since there are two points of intersection with the x axis, the quadratic equation has real and unequal roots. 

∴ Solution{-3, 3}