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
Example: Solve x2 + 3x - 10 = 0
x2 + 3x = 10
4x2 +12x = 40
4x2 + 12x + 9 = 40 + 9
4x2 + 12x + 9 = 49
2x + 3 = ±7
2x + 3 = 7 2x + 3 = 7
2x = 4 2x = -10
x = 2 x = -5
Try these:
(a) x2 - 2x - 13 =0
(b) 4x2 - 4x + 3 = 0
(c) x2 + 12x - 64 = 0
(d) 2x2 - 3x - 5 = 0

2. Mathematicians have been searching for a formula that yields prime numbers. One such formula was x2- 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.

Solution Summary

Step by step solutions to the questions is provided.

...solve using quadratic formula: solve by completing the square: solve by method. The expert solves the systems of equation by substitution and addition. ...

... Select some numbers for X, Substitute them in the formula, and see if prime numbers occur. ... An interesting method for solving quadratic equations came from India ...

... 1) y + By = 0 & y 2 xxx b) The substitution y = e mt leads to the quadratic equation emt ( m 2 ... A − 1) − 4B which has roots The general solution of this ...

... Just substitute -3 in place of x in the equation f(x)=2x2-7x+3 f(-3)=2(-3)2-7(-3)+ 3 On solving...Solve 2 x 2 − 3 x − 2 = 0 using the quadratic formula. 3). ...

... b) Solve by using the quadratic formula ... or x = 3 + 1 = 4 −b ± b 2 − 4ac The quadratic formula: 2a. ...Substitute t=1 into equation (1) s = −16 × 1 + 32 × 1 ...

...Solve the equations using either elimination or substitution. ... Cheers. 1. Solve by applying the Quadratic Formula; all radicals should be simplified as ...

... Therefore, you can just substitute v = 7 and h = 1to solve the quadratic equation: 1 = 7t − 5t 2 5t 2 − 7t + 1 = 0 Using the quadratic formula − ( −7 ...

... it to the original equation and determine if the rational equation is valid after substitution. ... An example of a quadratic equation with no solution is: ...