If the equations x2-4 x+5=0 and 2 x2-4[2 a+b] x+b=0(a, b ∈ R) have a common root, then maximum value of log b -2|2 a | lies in the interval

Question

If the equations x2-4 x+5=0 and 2 x2-4[2 a+b] x+b=0(a, b ∈ R) have a common root, then maximum value of log b -2|2 a | lies in the interval (A) (0,1) (B) (1,2) (C) (0,2) (D) (-1,1)

Tardigrade Admin · Accepted Answer

Θ Roots of equation x2-4 x+5=0 are imaginary ∴ Both roots are in common (2/1)=(4[2 a + b ]/4)=( b /5) ⇒ b =10 text and [2 a + b ]=2 ⇒[2 a ]=-8 ⇒-8 ≤ 2 a <-7 7<|2 a | ≤ 8 text maximum of log b -2|2 a |= log 8 8=1

Q. If the equations $x^{2} - 4 x + 5 = 0$ and $2 x^{2} - 4 [2 a + b] x + b = 0 (a, b \in R)$ have a common root, then maximum value of $lo g_{b - 2} ∣2 a ∣$ lies in the interval

$(0, 1)$

$(1, 2)$

$(0, 2)$

$(- 1, 1)$

Q. If the equations x2−4x+5=0 and 2x2−4[2a+b]x+b=0(a,b∈R) have a common root, then maximum value of logb−2​∣2a∣ lies in the interval

(0,1)

(1,2)

(0,2)

(−1,1)

Θ Roots of equation x2−4x+5=0 are imaginary ∴ Both roots are in common 12​=44[2a+b]​=5b​ ⇒b=10 and [2a+b]=2 ⇒[2a]=−8⇒−8≤2a<−7 7<∣2a∣≤8 maximum of logb−2​∣2a∣=log8​8=1

Q. If the equations $x^{2} - 4 x + 5 = 0$ and $2 x^{2} - 4 [2 a + b] x + b = 0 (a, b \in R)$ have a common root, then maximum value of $lo g_{b - 2} ∣2 a ∣$ lies in the interval

$(0, 1)$

$(1, 2)$

$(0, 2)$

$(- 1, 1)$