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Quadratic Formula

Quadratic Formula for ax 2 + bx + c = 0.

Example 1 Solve by using the quadratic formula.

(a) 2x2 − x − 3 = 0

(i) Factoring ,
2x2 − x − 3 = 0
(2x − 3)(x + 1) = 0

(ii) Completeing the square

(iii) Quadratic formula

a = 2, b = −1, c = 3,

(b) 3x2 + 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
(= x2).

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
2r2 + 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 in3?
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
2x2 − 24x + 64 = 20
2x2 − 24x + 44 = 0
x2 − 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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