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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Quadratic Equation

Black Advanced Problems in Mathematics · Mathematics · Quadratic Equation

Paragraph: **** Let f(x) = ax^2 + bx + c, a ≠ 0 , such that f(-1-x)...

Paragraph:
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Let f(x)=ax2+bx+c,a≠0f(x) = ax^2 + bx + c, a \ne 0, such that f(−1−x)=f(−1+x)∀x∈Rf(-1-x) = f(-1+x) \forall x \in R. Also given that f(x)=0f(x) = 0 has no real roots and 4a+b>04a + b > 0.
If f(x)=af(x) = a has two distinct real roots, then complete set of values of aa is :

Options

  1. A(1,∞)(1, \infty)
  2. B(−2,−1)(-2, -1)
  3. C(0,1)(0, 1)
  4. D(1,2)(1, 2)

    **Paragraph for Question Nos. 8 to 9**
    Consider the equation log⁡22x−4log⁡2x−m2−2m−13=0,m∈R\log_2^2 x - 4\log_2 x - m^2 - 2m - 13 = 0, m \in R. Let the real roots of the equation be x1,x2x_1, x_2 such that x1<x2x_1 < x_2.

Correct answer

A. (1,∞)(1, \infty)

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