+76 Find the sum of the roots of the quadratic x^2+7x-13=0
Find all values of x such that 2x^2 +9x- 5 = 0
Find all solutions to the equation 10x^2 - 7x - 6 = 0
Find all values of x such that 6 = 35/x - 49/x^2
What is the sum of the roots of the quadratic 4x^2 - 4x - 4?
Find the sum of all solutions to the equation 3x(x+4)= 66
One root of x^2 + 12x + k = 0 is twice the other root. Find k.
Not Homework i swear im just showing model problems i recieved.
+129849 Find the sum of the roots of the quadratic x^2+7x-13=0
In the form ax^2 + bx + c, the sum of the roots = -b / a
Here a = 1 and b = 7
So....the sum of the roots = -7/1 = -7
Find all values of x such that 2x^2 +9x- 5 = 0
We could use the quadratic formula to solve, but I like to see if this can factor, first
It will!!!
Factor as
(2x - 1) ( x + 5) = 0
Set each factor to 0 and solve for x
2x - 1 = 0 x + 5 = 0
add 1 to both sides subtract 5 from both sides
2x = 1 x = -5
divide both sides by 2
x = 1/2
The two solutions are in red
+129849 Find all solutions to the equation 10x^2 - 7x - 6 = 0
Again....let's see if we can factor
(5x - 6) ( 2x + 1) = 0
Set both faxctors to x and solve for x
5x - 6 = 0 2x + 1 = 0
5x = 6 2x = - 1
x = 6/5 x = -1/2
Find all values of x such that 6 = 35/x - 49/x^2
Here.....they are trying to be tricky.......multiply through by x^2 and we get
6x^2 = 35x - 49 rearrange as
6x^2 - 35x + 49= 0 see if we can factor
(3x - 7) (2x - 7) = 0
Set both factors to 0 and solve for x
3x - 7 = 0 2x - 7 = 0
3x = 7 2x = 7
x = 7/3 x = 7/2
+129849 What is the sum of the roots of the quadratic 4x^2 - 4x - 4?
Sum of the roots = - (-4) / 4 = 1
Find the sum of all solutions to the equation 3x(x+4)= 66
Simplify
3x^2 + 3x = 66
3x^2 + 3x - 66 = 0
Sum of the solutions (roots) = -3/3 = - 1
One root of x^2 + 12x + k = 0 is twice the other root. Find k.
This one is a little tricky.......
The sum of the roots is -12/ 1 = -12
Let one root = a and the other 2a
So.....the sum of the roots = -12
a + 2a = -12
3a = -12
a = -4
2a = 2(-4) = -8
Now.... in the form ax^2 + bx + c
The product of the roots is c /a
Here a = 1 and c = k
So.....the product of the roots is k /1 = k
So
(-4) (-8) = k = 32
