Chemistry

A. Roots Of Quadratic Equation

* General form : ax2 + bx + c = 0

* Highest power : 2

Eg 1:

Rewrite each of the following quadratic equations in the general form.

a. (5y – 7)2 = 54

b. 3t-72t-9=2t+9

c. 8 – x2 = 0

d. 2y- y4 = 3

e. 2x – 1 = 4x3x+5

Eg 2:

Determine if the given value is the root of the equation using the substitution & inpection method.

a. x2 – 4x + 3 = 0 ; x = 3

b. x2 – 5x + 6 = 0 ; x = 1

c. 2(1 – 3x)(x + 3) = 0 ; x = 3

Eg 3:

Given x = 2 and x = 3 are the roots for

x2 + px + q = 0, find the value of p and q.

B. Solving Quadratic Equation

* 3 methods:

* Factorization

* Using Formula

* x=-b±b2-4ac2a

* Completing the square

Eg 1:

Solve the following quadratic equations by factorization.

a. x2 + 2x – 15 = 0

b. 15x2 – 2(7x + 4) = 0

c. 4(x2 - 2) = x(x + 2)

d. 5 – 3k(3k +1) = k(9k + 50) - 30

e. tt-6= 2t+16t

Eg 2:

Find the roots of the equation below.

a. (x - 7)2 = 81

b. 36x2 – 49 = 0

Eg 3:

Find the roots of the following quadratic equations by using formula.

a. x + 1 = 6x-3

b. 4x2 + 12x = 9

c. 2x2 = 5x + 13

d. 11 – 7x = 4x2

e. 3x2 – 14x + 10 = 0

Eg 4:

By completing the square, solve the following quadratic equations.

Steps:

1. Rewrite as

ax2 + bx = c

2. Make the coefficient of x2 to 1

3. Add (coefficient of x2)2 to both sides of the equation.

a. x(x - 3) = 1

b. 3x2 + 8x – 2 = 0

c. 45x2 – 9x – 8 = 0

d. 2(2x2 + 1) = 11x

Eg 5:

Solve the following using appropriate method.

a. 6x2 + x – 2 = 0

b. 4x2 + 7x + 1 = 0

c. (x + 1)2 = 9

d. 15x2 = 19x – 6

Eg 6 :

The above diagram shows a rectangular piece of land PQRS. MN is a straight road linking the boundaries PQ and SR. The area of the land is 90km2. Given PM = 3x km, SN = 12km and NR = 4x km.

a. Show that 2x2 + 6x – 9 = 0.

b. Hence, find...