Graph

Sum

Graph the following quadratic equation and state their nature of solution

x2 – 4x + 4 = 0

#### Solution

Let y = x2 – 4x + 4

(i) Prepare the table of values for y = x2 – 4x + 4

 x – 4 – 3 – 2 – 1 0 1 2 3 4 x2 16 9 4 1 0 1 4 9 16 – 4x 16 12 8 4 0 – 4 – 8 – 12 – 16 4 4 4 4 4 4 4 4 4 4 y 36 25 16 9 4 1 0 1 4

(ii) Plot the points (– 3, 25) (– 2, 16) (– 1, 9) (0, 4) (1, – 1) (2, 0), (3, 1) and (4, 4)

(iii) Join the points by a free hand smooth curve.

(iv) The roots of the equation are the X-coordinates of the intersecting points of the curve with X-axis (2, 0) which is 2.

(v) Since there is only one point of intersection with the X-axis (2, 0).

∴ The solution set is 2.

The Quadratic equation x2 – 4x + 4 = 0 has real and equal roots.

Is there an error in this question or solution?

Chapter 3: Algebra – Exercise 3.15 [Page 137]

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