solve using the quadratic formula. if there are no real roots, say so.?

Question

8. x^2 + 9x +7 =0

10. 3x^2 + 7x - 6 = 0

14. 3= 7x - 4x^2

20. 3x^2 - 4x + 2 = 0

Answer 1

8) x^2 + 9x + 7 = 0

To determine if there are no real roots, we calculate the discriminate, b^2 - 4ac.
b^2 - 4ac = 9^2 - 4(1)(7) = 81 - 28 = [something positive].
So there are real roots.

x = [-9 +/- sqrt(81 - 4(7))]/2
x = [-9 +/- sqrt (53)] / 2
x = { [-9 + sqrt(53)]/2 , [-9 - sqrt(53)]/2 }

10. 3x^2 + 7x - 6 = 0

Solve for the discriminant.
b^2 - 4ac = 7^2 - 4(3)(-6) = [something positive]

x = [-7 +/- sqrt (49 - 4(3)(-6))] / 6
x = [-7 +/- sqrt (49 + 72)] / 6
x = [-7 +/- sqrt (121)] / 6
x = [-7 +/- 11] / 6
x = { [-7 + 11]/6 , [-7 - 11]/6 }
x = { [2/3] , -3 }

14. 3 = 7x - 4x^2

First, you have to put it in the proper form. Move everything to the left hand side, and in descending power order.

4x^2 - 7x + 3 = 0

Determine the discriminant.

b^2 - 4ac = 49 - 4(4)(3) = 49 - 48 = 1

x = [7 +/- sqrt (discriminant) ] / 8
x = [7 +/- sqrt (1)] / 8
x = [7 +/- 1] / 8
x = { (7 + 1)/8 , (7 - 1)/8}
x = { 1, 3/4 }

20. 3x^2 - 4x + 2 = 0

Discriminant: b^2 - 4ac = 16 - 4(3)(2) = 16 - 24 = -8, which is negative. Therefore, there are no real roots.

Answer 2

(8) -7/2 + √13 / 2 , -7/2 - √13 / 2 = -1.69722436226801, -5.30277563773199
(10) 2/3 , 3
(14)3/4 , 1
(20)2/3 +( √2/(3)) i , 2/3 -( √2/(3)) i

Answer 3

8. x^2+9x+7=0
7x^2=No root

10. 3x^2+7x-6=0
-18x^2=9x*-2x
3x^2+9x-2x-6
You make 2 groups
3x^2+9x__________-2x-6
3x(x+3)__________-2(x+3)
(3x-2) (x+3)=0
3x-2=0______________x+3=0
x=2/3_______________x=-3
x=((2/3), -3)

14.7x-4x^2
x(7-4x)=3
7-4x=3__________x=3
x=1_____________x=3
x=(1, 3)

20. 3x^2-4x+2=0
6x^2=No Root
Answers
8. No Root
10.x=((2/3), -3)
14.x=(1, 3)
20. No root

Answer 4

x equals -b plus or minus the square root of b squared minus 4ac over 2a....that'-s the formula, now do your own homework!