Question

Part 1: Create your own quadratic equation that cannot be solved by factoring, but can be solved using the quadratic formula. Identify the values of a, b, and c, and find the solutions using the quadratic formula.

Part 2: Using complete sentences, explain how you know that the equation from Part 1 cannot be solved by factoring, but can be solved by using the quadratic formula.

Answer 1

when you use all prime, non-one numbers for b and c, it cannot be factored most of the time


example
1x^2+7x+5
a=1
b=7
c=5
x=
`(-b+/- √(b^2-4ac) )/(2a)`
x=
`(-7+/- √(7^2-4(1)(5)) )/(2(1))`
x=
`(-7+/- √(49-20) )/(2)`
x=
`(-7+/- √(29) )/(2)`
x=
`(-7+ √(29) )/(2)` or
`(-7- √(29) )/(2)`

Answer 2

Part 1: x^2 - 5x -3 =2 where a is equal to 1, b is equal to -5 and c is equal to -5. It cannot be factored because we need 2 integers that will yield a product equal to -5 and the sum of the integers is equal to -5. Using the quadratic formula, we will obtain answers equal to:

x1 = (5+3√5)/2
x2 = (5-3√5)/2