10th Class Mathematics Quadratic Equations Question Bank Quadratic Equation

  • question_answer
    The graphs of\[\frac{1}{2}y={{x}^{2}}\]and\[y=rx+t\]intersect at two points (2, 8) and (6, 72). Find the quadratic equation in x whose roots are \[r+2\] and \[\frac{t}{4}-1\]

    A)  \[2{{x}^{2}}+6x-123=0\]                  

    B)  \[3{{x}^{2}}+33x+378=0\]

    C)  \[{{x}^{2}}-10x-121=0\]

    D)  \[{{x}^{2}}-11x-126=0\]

    Correct Answer: D

    Solution :

    (d): At (2, 8) and (6, 72),\[y=2{{x}^{2}}=rx+t\] 8 = 2r + t and 72 = 6r + t. Solving for r and t, r = 16 and t = ? 24. The required equation is that whose roots are 18 and ? 7. Sum of its roots = 11 Product of its roots = ? 126 \[\therefore \] The required equation is \[{{x}^{2}}-11x-126=0\]


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