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NDA - Quadratic Equation Test 1201
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NDA - Quadratic Equation Test 1201
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  • Question 1/5
    1 / -0.33
    The quadratic equation 3x2 – (k2 + 5k)x + 3k2 – 5k = 0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?
    Solutions

    The quadratic equation 3x2 – (k2 + 5k)x + 3k2 – 5k = 0, has real roots of equal magnitude and opposite sign.

    Then, sum of roots = 0 and

    From the above two condition no such value of k is possible.

  • Question 2/5
    1 / -0.33
    If p and q are the non-zero roots of the equation x2 + px + q = 0, then how many possible values can q have?
    Solutions

    p and q are the non-zero roots of the equation x2 + px + q = 0, then

    Sum of roots, p + q = -p or q = -2p

    Product of roots, pq = q , q = 0 or p =1

    For p = 1 , q = -2

    So, possible non-zero roots are 1 and -2.

  • Question 3/5
    1 / -0.33
    If sin θ and cos θ are the roots of the equation ax2 + bx + c = 0, then which one of the following is correct?
    Solutions

    Sum of the roots,  …i

    And product of the roots,  …ii

  • Question 4/5
    1 / -0.33
    Consider all the real roots of the equation x4 – 10x2 + 9 = 0. What is the sum of the absolute values of the roots?
    Solutions

    Sum of the absolute value of the roots =

  • Question 5/5
    1 / -0.33
    If the function f(x) = x2 – kx is monotonically increasing in the interval (1, ∞), then which one of the following is correct?
    Solutions

    function f(x) = x2 – kx is monotonically increasing

            

    Given that it is increasing in the interval (1, ∞).

          

    Now,

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