Answer:
[tex]0 = -2x^2 - 4x - 2[/tex]
Step-by-step explanation:
To solve this problem we must calculate the discriminant of each quadratic function.
Let [tex]ax ^ 2 + bx + c[/tex] be a quadratic function with a, b and c their real coefficients, then:
If [tex]b ^ 2 -4ac> 0[/tex] the function has 2 real solutions.
If [tex]b ^ 2 -4ac = 0[/tex] the function has 1 double real solution
If [tex]b ^ 2 -4ac <0[/tex] the function has complex solutions.
Now we calculate the discriminant for each of the functions:
[tex]0 = 2x^2 - 4x + 1[/tex]
[tex](-4) ^ 2 -4(2)(1) = 8[/tex] (Two real solutions)
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[tex]0 = 2x^2- 5x + 3[/tex]
[tex](-5) ^ 2 -4(2)(3) = 1[/tex] (Two real solutions)
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[tex]0 = -2x^2 - 4x - 2[/tex]
[tex](-4) ^ 2 -4(-2)(- 2) = 0[/tex] (A real double solution)
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[tex]0 = -2x^2 - 3x - 1[/tex]
[tex](-3) ^ 2 -4(-2)(- 1) = 1[/tex] (Two real solutions)
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The equation we want is:
[tex]0 = -2x^2 - 4x - 2[/tex]
