Respuesta :
If the quadratic function f(x) = [tex]x^2[/tex] - 16x + 73 is equal to zero when
x = a +bi, then the value of a = 8 and the value of b = ±3
The given quadratic function is
f(x) = [tex]x^2[/tex] - 16x + 73
The value of a = 1
The value of b = -16
The value of c = 73
The quadratic equation = [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values in the equation
= [tex]\frac{+16+/-\sqrt{(-16)^2-4(1)(73)} }{2(1)}[/tex]
Do the arithmetic operations
= [tex]\frac{+16+/-\sqrt{256-292} }{2}[/tex]
Subtract the terms
= [tex]\frac{16+/-\sqrt{-36} }{2}[/tex]
= (16±6i) / 2
= 8 ± 3i
Hence, if the quadratic function f(x) = [tex]x^2[/tex] - 16x + 73 is equal to zero when
x = a +bi, then the value of a = 8 and the value of b = ±3
The complete question is:
The quadratic function f(x) = [tex]x^2[/tex] - 16x + 73 is equal to zero when
x = a +bi, find the value of a and b
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