a. between -3 and -2 and between 0 and 1
b. between -1 and 0 and between 2 and 3
c. no real solutions
d. -1, 1
b. between -1 and 0 and between 2 and 3
c. no real solutions
d. -1, 1
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Graphing is a pain in the backside. Use wolfram alpha to show graphs.
However, using algebra (a sneaky tactic) there are no real solutions.
However, using algebra (a sneaky tactic) there are no real solutions.
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A picture helps.
Put your quadratic in standard form: ax^2 + bx + c = 0
x^2 + 2x = - 2
x^2 + 2x + 2 = 0
a = 1, b = 2, c = 2
Check out the discriminant of the quadratic formula, b^2 - 4ac, to see if this thing has real roots.
b^2 - 4ac = 2^2 - 4(1)(2) = 4 - 8 = - 4.
The discriminant is negative. Your parabola has complex roots.
Sketch your parabola opening upward, with the vertex above the x-axis.
Put your quadratic in standard form: ax^2 + bx + c = 0
x^2 + 2x = - 2
x^2 + 2x + 2 = 0
a = 1, b = 2, c = 2
Check out the discriminant of the quadratic formula, b^2 - 4ac, to see if this thing has real roots.
b^2 - 4ac = 2^2 - 4(1)(2) = 4 - 8 = - 4.
The discriminant is negative. Your parabola has complex roots.
Sketch your parabola opening upward, with the vertex above the x-axis.