Find solutions of the equation x^2 - 1x + 7 = 0 and express them in the form a + bi.?

Question

I've done problems like these with parenthesis but never without them. Can I use the quadratic formula for this? Thanks.

Answer 1

You can use the quadratic formula or you can complete the square.
It's already in the form
ax^2 + bx + c = 0
x^2 - 1x + 7 = 0
a = 1, b = -1 and c = 7
[-b +/- sqrt(b^2 -4ac)]/(2a)
= [-(-1) +/- sqrt((-1)^2 -4(1)(7))]/(2*1)
= [1 +/- sqrt(1-28)]/2
= [1 +/- sqrt(-27)]/2
= [1 +/- i sqrt(9*3)]/2
= [1 +/- 3i sqrt(3)]/2
= 1/2 + (3i/2) sqrt(3) or 1/2 - (3i/2) sqrt(3)

Answer 2

You must used the general theory of the equation with degree=2,ax^2+bx+c=0 and discriminant =b^2-4ac<0

Answer 3

Yes you can, but the solution may not have complex roots.

Study the discriminant - b2-4ac = (-1)^2-4(1)(7) = 1-28

You take it from here.

Answer 4

Just use the quadratic formula.

1/2 + sqrt(27)/2 * i
1/2 - sqrt(27)/2 * i

Answer 5

x^2 - x + 7

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-(-1) ± sqrt((-1)^2 - 4(1)(7)))/(2(1))
x = (1 ± sqrt(1 - 28))/2
x = (1 ± sqrt(-27))/2
x = (1 ± sqrt(-9 * 3))/2
x = (1 ± 3isqrt(3))/2

x = (1/2) + ((3/2)sqrt(3))i or (1/2) - ((3/2)sqrt(3))i

if you have mistyped anything, just use the same formula.

Answer 6

1/2 + ((3 * 3^ 0.5)/2)* i and 1/2 - ((3 * 3^ 0.5)/2)* i