complex numbers and discriminants help?

x² - 3x + 1 = 0

Take the middle term (3) and half it (3/2) and now square the result (3/2)² = 9/4 and now add and subtract this into the equation:

x² - 3x + (9/4) - (9/4) + 1 = 0

The first three terms make a perfect square:

(x - (3/2))² - (9/4) + 1 = 0

(x - (3/2))² - (5/4) = 0

(x - (3/2))² = 5/4

Taking square on both sides:

x - (3/2) = ±√(5)/2

x = (3/2) ±√(5)/2

x = (3±√(5))/2 Answer. (option B & D).

in the equation 4x^2 - x + 5 = 0 a = 4, b = -a million and c = 5 The discriminant is b^2 - 4ac so as that's -a million^2 - 4(4)(5) = a million - eighty = -seventy 9 So earlier you do something you be attentive to the respond is going to be B yet enable's artwork it out besides. The roots of the quadratic are -b +/- ? -seventy 9 throughout 2a now 2a of direction is two*4 = 8 and -b is - -a million that's +a million. So the respond is a million +/- ? -seventy 9 throughout 8 Sorry in case that's no longer glaring: a million +/- ? -seventy 9 throughout 8 skill: (a million + ? -seventy 9) /8 is without doubt considered one of the roots. the different root is: (a million - ? -seventy 9) /8. wish that facilitates.

x^2-3x+1=0

x = (-(-3) ± √( (-3)² - 4(1)(1) ) / (2(1))
x = (3 ± √ (9 - 4)) / 2
x = (3 ± √ 5) /2
Answer is b & d

x^2 - 3x + 1 = 0

x = (-(-3) +/- sqrt(3^2 - 4*1*1))/2(1)
= (3 +/- sqrt(5))/2

(3 + sqrt(5))/2 and (3 - sqrt(5))/2