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Please please please help

Please please please help-example-1

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Answer:

I. B. true

II. A true

Explanation:

we can use the quadratic equation:


x=\frac{-b+-\sqrt{b^(2)-4*a*c}}{2*a}

we have:

1)
x^(2) -4x+5

a=1 b=-4 c=5


x=\frac{-(-4)+-\sqrt{(-4)^(2)-4*1*5}}{2*1} \\\\x=(4+-√(-4))/(2) \\\\x=(4+-√(4) i)/(2)\\\\x=(4+-2i)/(2) \\\\x_(1) =2-i\\\\x_(2) =2+i

the quadratic expression has two complex factors.

2)
x^(2) -5x+14

a=1 b=-5 c=14


x=\frac{-(-5)+-\sqrt{(-5)^(2)-4*1*14}}{2*1} \\\\x=(5+-√(-31))/(2) \\\\x=(5+-√(31) i)/(2)\\\\x_(1) =(5-√(31)i )/(2)\\ \\x_(2) =(5+√(31)i )/(2)

the solution of
x^(2) -5x+14 are


x_(1) =(5-√(31)i )/(2)\\\\or\\x_(2) =(5+√(31)i )/(2)

3)
2x^(2) -8x+5

a=2 b=-8 c=5


x=\frac{-(-8)+-\sqrt{(-8)^(2)-4*2*5}}{2*2} \\\\x=(8+-√(24))/(4) \\\\x=(8+-2√(6))/(4)\\\\x_(1) =2-(√(6))/(2)\\ \\x_(2) =2+(√(6))/(2)

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