Download 1. An interesting method for solving quadratic equations came from

1. An interesting method for solving quadratic equations came from India. The steps are (a) Move the constant term to the right side
of the equation. (b) Multiply each term in the equation by four times the coefficient of the x2 term. (c) Square the coefficient of the
original x term and add it to both sides of the equation. (d) Take the square root of both sides. (e) Set the left side of the equation
equal to the positive square root of the number on the right side and solve for x. (f) Set the left side of the equation equal to the
negative square root of the number on the right side of the equation and solve for x.
A) x2 – 2x-13=0
B) 4x2 - 4x+3=0
C) x2 +12x-64=0
D) 2x2 -3x-5=0
(A) x^2 - 2x = 13
4x^2 - 8x = 52
4x^2 - 8x + 4 = 56
(2x - 2)^2 = 56
2x - 2 = 56 = 214
2(x - 1) = 214
x - 1 = 14
x = 1 + 14
2x - 2 = 56 = -214
2(x - 1) = -214
x - 1 = -14
x = 1 - 14
(B) x^2 - 4x = -3
4x^2 - 16x = -12
4(x^2 - 4x) = -12
x^2 - 4x = -3
x^2 - 4x + 4 = 1
(x - 2)^2 = 1
x-2=1
x = 2 + 1 = 2 + 1 = 3
x - 2 = -1
x = 2 - 1 = 2 - 1 = 1
(C) x^2 + 12x = 64
4x^2 + 48x = 256
4x^2 + 48x + 144 = 400
(2x + 12)^2 = 400
2x + 12 = 400
2x + 12 = 20
x=4
2x + 12 = -20
x = -16
(D) 2x^2 - 3x = 5
x^2 - 1.5x = 2.5
4x^2 - 6x = 10
4x^2 - 6x + 2.25 = 12.25
(2x - 1.5)^2 = 12.25
2x - 1.5 = 12.25
2x - 1.5 = 3.5
x = 2.5
2x - 1.5 = -3.5
x = -1
2. Mathematicians have been searching for a formula that yields prime numbers. One such formula was x^2 - x +41. Select some
numbers for x, substitute them in the formula, and see if prime numbers occur. Try to find a number for x that when substituted in
the formula yields a composite number.
Let p(x) = x^2 - x + 41
Lets plug in x = 1, 2, 3, 5, 7, 10, 12 and 20 and see if we get prime numbers
p(1) = 1^2 - 1 + 41 = 41 (Prime)
p(2) = 2^2 - 2 + 41 = 43 (Prime)
p(3) = 3^2 - 3 + 41 = 47 (Prime)
p(5) = 5^2 - 5 + 41 = 61 (Prime)
p(7) = 7^2 - 7 + 41 = 83 (Prime)
p(10) = 10^2 - 10 + 41 = 131 (Prime)
p(12) = 12^2 - 12 + 41 = 173 (Prime)
p(20) = 20^2 - 20 + 41 = 421 (Prime)
... The list goes on, yielding prime numbers up to x = 40
Now, let x = 41. Then
p(41) = 41^2 - 41 + 41 = 41^2 = 1681, which obviously is not a prime.