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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:
****
Let

f(x) = ax^2 + bx + c, a \ne 0

, such that

f(-1-x) = f(-1+x) \forall x \in R

. Also given that

f(x) = 0

has no real roots and

4a + b > 0

.

The sum of maximum value of

x_1

and minimum value of

x_2

is :

Options

A $513/8$
B $513/4$
C $1025/8$
D $257/4$

**Paragraph for Question Nos. 10 to 11**
The equation $x^4 - 2x^3 - 3x^2 + 4x - 1 = 0$ has four distinct real roots $x_1, x_2, x_3, x_4$ such that $x_1 < x_2 < x_3 < x_4$ and product of two roots is unity, then :

Correct answer

D. $257/4$

**Paragraph for Question Nos. 10 to 11**
The equation $x^4 - 2x^3 - 3x^2 + 4x - 1 = 0$ has four distinct real roots $x_1, x_2, x_3, x_4$ such that $x_1 < x_2 < x_3 < x_4$ and product of two roots is unity, then :

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