The value of m for which expression (2 x2-5 x+3/4 x-m) can take all real values for x ∈ R- (m/4) is

Question

The value of m for which expression (2 x2-5 x+3/4 x-m) can take all real values for x ∈ R- (m/4) is (A) (4,6) (B) [4,6] (C) R (D) R- 4,6

Tardigrade Admin · Accepted Answer

y=(2 x2-5 x+3/4 x-m) ⇒ 4 x y-m y=2 x2-5 x+3 ⇒ 2 x2-x(5-4 y)+m y+3=0 D ≥ 0 (5-4 y)2-4 ⋅ 2(m y+3) ≥ 0 ⇒ 16 y2+y(40-8 m)+1 ≥ 0 D ≤ 0 (40-8 m)2-4 ⋅ 16 ≤ 0 m ∈[4,6] text But x ≠ m / 4 text so, m ∈(4,6)

Q. The value of $m$ for which expression $\frac{2 x ^{2} - 5 x + 3}{4 x - m}$ can take all real values for $x \in R - {\frac{m}{4}}$ is

$(4, 6)$

$[4, 6]$

$R$

$R - {4, 6}$

Q. The value of m for which expression 4x−m2x2−5x+3​ can take all real values for x∈R−{4m​} is

(4,6)

[4,6]

R

R−{4,6}

y=4x−m2x2−5x+3​⇒4xy−my=2x2−5x+3 ⇒2x2−x(5−4y)+my+3=0 D≥0 (5−4y)2−4⋅2(my+3)≥0 ⇒16y2+y(40−8m)+1≥0 D≤0 (40−8m)2−4⋅16≤0 m∈[4,6] But x=m/4 so, m∈(4,6)

Q. The value of $m$ for which expression $\frac{2 x ^{2} - 5 x + 3}{4 x - m}$ can take all real values for $x \in R - {\frac{m}{4}}$ is

$(4, 6)$

$[4, 6]$

$R$

$R - {4, 6}$