Write three quadratic equations one having two distinct real solutions, one having no real solution and one having exactly one real solution.
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quadratic equation having two distinct real solutions : x² + 7x + 10 = 0
[ it has two distinct {e.g., -5 and -2 } real solutions ]
quadratic equation having no real solutions : x² + 1 = 0
[ x² + 1 = 0, x² = -1 , here LHS is positive and RHS is negative. so, this quadratic equation having no real solutions it has imaginary solutions]
quadratic equation having one real solutions : x² - 6x + 9 = 0
[ x² - 6x + 9 = x² - 2.3.x + (3)² = (x - 3)² = 0 hence, it has only one real solution e.g., x = 3]
[ it has two distinct {e.g., -5 and -2 } real solutions ]
quadratic equation having no real solutions : x² + 1 = 0
[ x² + 1 = 0, x² = -1 , here LHS is positive and RHS is negative. so, this quadratic equation having no real solutions it has imaginary solutions]
quadratic equation having one real solutions : x² - 6x + 9 = 0
[ x² - 6x + 9 = x² - 2.3.x + (3)² = (x - 3)² = 0 hence, it has only one real solution e.g., x = 3]
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In the attachment I have answered this problem. I have given three quadratic equations as per the given conditions. See the attachment for detailed solution.
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