X2 - X - 6 = 0
what two factors of - 6 add up to - 1 ?
(X + 2)(X - 3)
============
(- 2, 0 ) and (3, 0 )
------------------------------solution set of points
An equation with the solution set 1 and 3 can be written in factored form as (x-1)(x-3) = 0. When expanded, this equation becomes x^2 - 4x + 3 = 0. Therefore, the equation x^2 - 4x + 3 = 0 has the solution set 1 and 3.
'x' must be zero, so the solution set is [ 0 ].
Yes. Consider x2 ≥ 0
Yes. x2-4x+4=0 (x-2)(x-2)=0 x=2
The algebraic equation becomes x2 - x = 2 (or) x2 - x - 2 = 0 This has the solution (x-2)(x+1) = 0 so the answer is either 2 or -1.
An equation with the solution set 1 and 3 can be written in factored form as (x-1)(x-3) = 0. When expanded, this equation becomes x^2 - 4x + 3 = 0. Therefore, the equation x^2 - 4x + 3 = 0 has the solution set 1 and 3.
do it yourself
x2 + 49 = 0 ∴ x2 = -49 ∴ x = 7i
Nope. Consider x2+0x+1=0. This means x2+1=0. This has two solutions, but they are complex numbers: +i and -i, where i is the squareroot of -1. How about x2+0x+0=0? This means x2=0. This has two solutions, sure, but they aren't distinct. In this case, x=0 for both solutions, so we just consider them one solution.
11
There are no real solutions to this equation because you cannot take the square root of a negative number. However,x2 + 4 = 0x2 = -4sqrt(x2) = sqrt(-4)x = 2i, -2ihere are the imaginary solutions.
X2 - 3X - 4 = 0factored(X + 1)(X - 4)----------------X = - 1X = 4-------------------(- 1, 0) and (4, 0)================solution set of X interception points
Using the quadratic formula, you get the complex answers of 1 + 2i and 1 - 2i
x = 2 or -2
For the equation x2- 10x - k equals 0, you can solve this by knowing that if there is only one solution then the discriminant b2 - 4ac must be equal to 0. In this equation, a is 1, b is 10 and c is k This equation becomes 100 - 4k equals 0, and k is 25.
Using the quadratic formula, I found the solution set is x=2,x=-9
I'll show work. X2-8x-4=0. X2-8x=4. X-8x=2. -7x=2. X=-(2/7).