2X^2+3X+1
d^2+8d+7
2a^2+5a+3
3x^2-x-4
2n^2+n-6
x^2+5x-14
5x^2-2x-7
7n^2+9n+2
3x^2+8x+4
7a^2-30a+8
7n^2+9n+2
(7n + 2)(n + 1)
We do not do your work for you. Once you have answered your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?
Try factoring the numerical term and the numerical aspect of x^2. See how they would combine to add/subtract to get middle term.
I hope this helps.
To find the solutions for the given quadratic equations, we can use the quadratic formula. The quadratic formula states that for any quadratic equation in the form of ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Let's solve each equation using this formula:
1. 2x^2 + 3x + 1:
a = 2, b = 3, c = 1
Using the quadratic formula:
x = (-3 ± √(3^2 - 4*2*1)) / (2*2)
Simplifying:
x = (-3 ± √(9 - 8)) / 4
x = (-3 ± √1) / 4
x = (-3 ± 1) / 4
The solutions are:
x = (-3 + 1) / 4 = -1/2
x = (-3 - 1) / 4 = -1
2. d^2 + 8d + 7:
a = 1, b = 8, c = 7
Using the quadratic formula:
d = (-8 ± √(8^2 - 4*1*7)) / (2*1)
Simplifying:
d = (-8 ± √(64 - 28)) / 2
d = (-8 ± √36) / 2
d = (-8 ± 6) / 2
The solutions are:
d = (-8 + 6) / 2 = -1
d = (-8 - 6) / 2 = -7
3. 2a^2 + 5a + 3:
a = 2, b = 5, c = 3
Using the quadratic formula:
a = (-5 ± √(5^2 - 4*2*3)) / (2*2)
Simplifying:
a = (-5 ± √(25 - 24)) / 4
a = (-5 ± √1) / 4
a = (-5 ± 1) / 4
The solutions are:
a = (-5 + 1) / 4 = -1
a = (-5 - 1) / 4 = -3/2
4. 3x^2 - x - 4:
a = 3, b = -1, c = -4
Using the quadratic formula:
x = (-(-1) ± √((-1)^2 - 4*3*(-4))) / (2*3)
Simplifying:
x = (1 ± √(1 + 48)) / 6
x = (1 ± √49) / 6
x = (1 ± 7) / 6
The solutions are:
x = (1 + 7) / 6 = 2
x = (1 - 7) / 6 = -1
And so on for the remaining equations using the same process.