Question 549034
Find the complex zeros of the quadratic function.
h(x) = x2 - 12x + 45
*[invoke solve_quadratic_equation 1,-12,45
x = 6 ± 3i
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Without solving, determine the character of the solutions of the equation.
x2 - 2x + 2 = 0
Determinant = b^2 - 4ac = 4 - 8 = -4
Det < 0 --> 2 complex solutions (they're always conjugates)
c
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Answer
a. two unequal real solutions
b. a repeated real solution
c. two complex solutions that are conjugates of each other 
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Find the x-intercept
f(x) = -x2 + 7x - 12
-(x-3)*(x-4) = 0
x = 3, x = 4
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Find the x-intercepts.
f(x) = 2x^2 - 10x - 12
{{{x^2 - 5x - 6 = 0}}} (divided by 2)
(x-6)*(x+1) = 0
x = -1, x = 6
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Solve.
x2 + 5 = 230
x^2 = 225
x = ± 15
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Without solving, determine the character of the solutions of the equation.
x2 + 7x + 6 = 0
Determinant = b^2 - 4ac = 7^2 - 4*1*6
Det = 25
Det > 0 --> 2 real solutions (not equal)
b
Answer
a. a repeated real solution
b. two unequal real solutions
c. two complex solutions that are conjugates of each other