Ws Nd1 Quad Eq _1_ Factoriong Method

Quadratic Equations (Factoring Method) How to solve quadratic equation of the form ax2 + bx + c = 0 with factoring If the given quadratic equation can be factored, the equations can be solved as follows: If ax 2 + bx + c = ( px + q )(rx + s ) ax 2 + bx + c = 0

( px + q )(rx + s ) = 0

px + q = 0 rx + s = 0

x=

q p s r

EXERCISE 1 1. Solve the following quadratic equations using the factoring method: (a) 2 x 2 + 7 x + 3 = 0

(b) 3 x 2 + 4 x + 1 = 0

Ans: x =

and

Ans: x =

.

(c) 2 x 2 + x 4 = 0

and

(d) 6 x 2 7 x + 2 = 0

Ans: x =

and

Ans: x =

.

(e) x 2 5 x + 3 = 0

and

.

and

.

(f) 6 x 2 + 5 x 6 = 0

Ans: x =

and

.

Ans: x =

.

2. Solve the following quadratic equations using the factoring method: (a) 14 x 2 29 x 12 = 0

(b) x 2 6 x + 9 = 0

Ans: x =

and

Ans: x = 3 and

.

.

3. Solve the following quadratic equations using the factoring method: (a) x 2 81 = 0

(b) x 2 25 = 0

Ans: x = 9 and

Ans: x =

and

.

Ans: x = 1.73 and

.

.

(c) x 2 2 = 0

(d) x 2 3 = 0

Ans: x = 1.414 and

.

(e) x 2 + 25 = 0

(d) x 2 + 1 = 0

Ans:

Ans:

.

..

4. Solve the following quadratic equations using the complete square method: (a) x 2 2 x = 0

(b) x 2 5 x = 0

Ans: x = 2 and

.

Ans: x = 5 and

.

EXERCISE 2 1. Solve the following quadratic equations using the complete square method: (a) 2 x 2 + 7 x + 3 = 0

(b) 3 x 2 + 4 x + 1 = 0

Ans: x =

and

.

(c) 2 x 2 + x 4 = 0

Ans: x =

and

.

Ans: x =

and

..

Ans: x =

and

..

Ans: x =

and

..

(d) 6 x 2 7 x + 2 = 0

Ans: x =

and

.

(e) x 2 5 x + 3 = 0

(f) 6 x 2 + 5 x 6 = 0

Ans: x =

and

..

(d) x 2 81 = 0

(d) x 2 5 x = 0

Ans: x =

and

.