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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

For the quadratic polynomial f(x) = 4x^2 - 8ax + a , the...

For the quadratic polynomial

f(x) = 4x^2 - 8ax + a

, the statements(s) which hold good is/are :

Options

AThere is only one integral ' $a$ ' for which $f(x)$ is non-negative $\forall x \in R$
BFor $a < 0$ , the number zero lies between the zeroes of the polynomial
C $f(x) = 0$ has two distinct solutions in $(0, 1)$ for $a \in (\frac{1}{4}, \frac{4}{7})$
DThe minimum value of $f(x)$ for minimum value of $a$ for which $f(x)$ is non-negative $\forall x \in R$ is $0$ .

Correct answer

A. There is only one integral ' $a$ ' for which $f(x)$ is non-negative $\forall x \in R$

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