Page 22 - Mathematics Class - X

ACTIVITY 2.3

OBJECTIVE
To obtain the solution of a quadratic equation (x + 4x = 60) by completing the square geometrically.
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MATERIALS REQUIRED

Hardboard Scissors
Glazed papers Marker
Adhesive White chart paper

PRE-REQUISITE KNOWLEDGE
1. Concept of quadratic equation and its solutions
2. Knowledge to solve quadratic equation by completing the square

THEORY

1. An equation of the form ax + bx + c = 0, a ≠ 0 is called quadratic equation, where a, b and c are constants.
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A real number a is said to be a root of a quadratic equation ax + bx + c = 0, where a ≠ 0, if aa + ba + c = 0.
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2. a is also called the solution of quadratic equation. Any quadratic equation can have at most two roots.

PROCEDURE

1. Take a cardboard and paste a white chart paper on it.
2. Draw a square ABCD of side of length x units and paste it on the cardboard (see Fig. (a) on next page).

3. Divide it into 36 unit squares with a marker.
4. Now each side of square ABCD, i.e. x has been divided into 6 equal units. Hence, the length of x can be
considered as 6 units.

5. Along with each side of the square (outside) paste rectangles BEPC, AJGB, AHKD, CNMD of paper of
dimensions x × 1, i.e., 6 × 1 and divide each of them into 6 squares of unit side with the help of a marker
(see Fig. (b) on next page).
6. Draw four squares each of side 1 unit on a paper, cut them out and paste each unit square on each corner and
shade them with a marker, these are BEFG, AHIJ, DKLM, CNOP (see Fig. (b) on next page).

7. Draw another square of dimension 8 × 8 and divide it into 64 unit squares identical to those in Fig. (c).
8. From Fig. (b), it can be observed that the total area represented by the square is,

Area of ABCD + Area of four squares of 1 × 1 + Area of rectangles (AJGB, AHKD, BEPC, CNMD)
= x × x + 4 × (1 × 1) + 4 (x × 1)

= x + 4x + 4
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i.e. total area of Fig. (b) is equal to x + 4x + 4.
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