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Equations and Inequalities Test - 22
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Equations and Inequalities Test - 22
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  • Question 1/10
    4 / -1
    If the roots of the equation bχ2 + cχ + a = 0 is imaginary, then for all real values of χ, the expression 3b2 χ2 + 6bcχ + 2c2 is
    Solutions

  • Question 2/10
    4 / -1
    If a, b and c are in GP, then the equation aχ2 + 2bχ + c = 0 and dχ2 + 2eχ + f = 0 have a common root, if d/a, e/b and f/c are in
    Solutions

  • Question 3/10
    4 / -1
    If ax2 + bχ + c = 0 and 2χ2 + 3χ + 4 = 0 have a common root, where a, b, c ∈ N (set of natural numbers), then the least value of a + b + c is
    Solutions

  • Question 4/10
    4 / -1

    Solutions

  • Question 5/10
    4 / -1
    The quadratic equations χ2 - 6χ + a = 0 χ2 - cχ + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then, the common root is
    Solutions

  • Question 6/10
    4 / -1
    Let a, b and c be real. If aχ2 + bχ + c = 0 has two real roots α and β where α < - 1 and β > 1 , then

    Solutions

  • Question 7/10
    4 / -1
    All the values of m for which both roots of the equation χ2 - 2mχ + m2 - 1 = 0 are greater than - 2 but less than 4 lie in the interval
    Solutions

  • Question 8/10
    4 / -1
    The values of k, for which the equations χ2 - kχ - 21 = 0 and χ2 - 3kχ + 35 = 0 will have a common roots, is
    Solutions

  • Question 9/10
    4 / -1
    If the both the root of the quadratic equation χ2 - 2kχ + k2 + k - 5 = 0 are less than 5, then k lies in the interval
    Solutions

  • Question 10/10
    4 / -1
    If χ is real, then the value of

    Solutions

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