Question

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

(i) x² – 9x + 20 = 0

(ii) x² – 4x + 4 = 0

Answer 1

(i)

Step 1:

Points to be plotted : (-4, 72), (-3, 56), (-2, 42), (-1, 30), (0, 20), (1, 12), (2, 6), (3, 2), (4, 0) 

Step 2: 

The point of intersection of the curve with x axis is (4, 0) 

Step 3:

The roots are real & unequal 

∴ Solution {4, 5}

(ii) 

Step 1: Points to be plotted : (-4, 36), (-3, 25), (-2, 16), (-1, 9), (0, 4), (1, 1), (2, 0), (3, 1), (4, 4) 

Step 2: The point of intersection of the curve with x axis is (2, 0) 

Step 3:

Since there is only one point of intersection with x axis, the quadratic equation x – 4x + 4 = 0 has real and equal roots. 

∴ Solution{2, 2}