Page 85 - Mathematics_Form_Two

Algebra

Exercise 4�7 Solving quadratic equations by using
quadratic general formula
1. To each of the following expressions
add a term which will make it a The method of solving quadratic equations
perfect square and write the result by completing the square can be used to
in the form (x k+ 2 ) . derive the general formula for solving
quadratic equations as follows.
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3
(a) x − 12x (b) a + a 2
2
2
2 From, ax + bx + c = 0, a ≠ 0.
7 Divide each term by a to get,
(c) x + x (d) x − 4x
2
2
2 x + 2 b x + c = 0 Mathematics for Secondary Schools
a a
(e) x − x (f) x + 5x c
2
2
Subtract from both sides to obtain,
4 a
2
(g) p + 12p (h) n + n
2
3 b c
x 2 x + = -
t a a
(i) t + (j) x + 3x
2
2
2  b  2
Add   to both sides of the equation.
2. Solve each of the following  2a 
quadratic equations by completing 2 b æ b 2 c ö æ b ö 2
the square. That is, x a x + + ç 2 ÷ = - + ç 2a è a è ÷ ø .
a ø
(a) x 2 2x + - 15 = 0. Factorize the left-hand side and simplify
(b) 4v 2 8v - += 0. the right-hand side to obtain,
3

(c) x 2 11x - - 3 = 0.  x + b   2 = − c + b 2 = b − 2 4ac
 2a  a 4a 2 4a 2
(d) 62cc- - 2 = 0 Take the square root of both sides to get,

2
(e) x 2 7x - + 11= 0. b b - 4ac
x + 2 =± 2
(f) 3s - 2 6s - += 4a a
10
2 2
b b - 4b − 4ac ac
(g) 11 aa-- 2 = 0 x + =± 
a
2 4a 2a 2
(h) p + 2 11 6p= b
Subtract from both sides to get,
(i) 10x + 8x − 2 = 0 2a
2

(j) 3h −24h − 3 = 0
2
(k) 5s −15s + 5 = 0
2

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 79 11/10/2024 20:12:04
MATHEMATIC F2 v5.indd 79