10th Class Mathematics Related to Competitive Exam Question Bank Quadratic Inequation

  • question_answer
    Find the values that x can take in \[{{x}^{2}}-2x+3\ge 0\]

    A)  \[[2,3]\]            

    B)  \[[1,2]\]

    C)  \[x\ge -1\]and \[x\in \left( -\infty ,1 \right)\cup \left( 2,\infty  \right)\]

    D)  \[\left( -\infty ,1 \right)\cup \left( 2,\infty  \right)\]

    Correct Answer: D

    Solution :

    (d): General solution for \[(x-a)(x-b)\ge 0\]\[b>a\,;\] when roots are ?a? and ?b? is given as\[x\in (-\infty ,a)\cup (b,\infty )\]. The specific solution here (given a = 1, b = 2) becomes\[x\in (-\infty ,1)\cup (2,\infty )\]


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