# Quadratic Formula

Quadratic Formula for ax^{2} + bx + c = 0.

**Example 1** Solve by using the quadratic formula.

(a) 2x^{2} − x − 3 = 0

(i) Factoring ,

2x^{2} − x − 3 = 0

(2x − 3)(x + 1) = 0

(iii) Quadratic formula

a = 2, b = −1, c = 3,

(b) 3x^{2} + 7x + 3 = 0

(c)

Our goal is to remove the denominator to make this
equation into one to

which you can apply the quadratic formula . That is multiplying by its LCD

(= x^{2}).

Be sure to exclude x = 0 which makes the bottom of the
original equation

zero .

**Example 2 **Solve for ???

(a) Prob 51

Or use the quadratic formula .

(b) Prob 53 without π

A = 2r(r + h), for r

A = 2r(r + h)

2r(r + h) = A

2r^{2} + 2hr − A = 0

**Remark 1** Interesting point about discriminant. Will
be added

**Example 3** Refer to Example 12 in the text book. A
box with an open top is

to be constucted by cutting 4-inch squares from the corners of a rectangular

sheet of tin whose length is twice its width. What size sheet will produce a

box having a volume of 80 in^{3}?

length is twice width ) width => x, length = 2x

and the height is 4.

Area of the base = width times length = (x − 2 · 4)(2x − 2
· 4)

Volume = Area · height = 4(x − 2 · 4)(2x − 2 · 4) = 80

4(x − 2 · 4)(2x − 2 · 4) = 80

(x − 8)(2x − 8) = 20

2x^{2} − 24x + 64 = 20

2x^{2 }− 24x + 44 = 0

x^{2} − 12x + 22 = 0

Please check that your answer makes sense or not. Since we
are cutting 4inch

from the corner
hence

can’t be your answer.

Quadratic Formula for ax ^{2} + bx + c = 0.

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