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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 4inch 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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