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Equation (x+2)(x+3)(x+8)(x+12)=4x^2 has ...

Equation `(x+2)(x+3)(x+8)(x+12)=4x^2` has (A) four real and distinct roots (B) two irrational roots (C) two integer roots (D) two imaginary roots

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Knowledge Check

  • Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots

    A
    Two distinct positive real roots
    B
    Two equal roots
    C
    One positive and one negative root
    D
    No real roots

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    The quadratic equation ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x+b))/((a-c)(b-c))=1 has (A) Two real and distinct roots (B) Two Equal roots (C) Non Real Complex Roots (D) Infinite roots

    f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

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    If p,q,r epsilon R and are distinct the equation (x-p)^5+(x-q)^5+(x-r)^5=0 has (A) four imaginary and one real root (B) two imaginary and three real roots (C) all the roots real (D) none of these

    If p and q are odd integers, then the equation x^2+2px+2q=0 (A) has no integral root (B) has no rational root (C) has no irrational root (D) has no imaginary root

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