If the set of values of p for which roots of the equation 2 x2-(2 p-3) x+2=0 are 2(-2/ sin -1 α) and 2(2/π) sin -1 α for some value of α in [-1,1] is [a, b], then 12(a+b) is

Question

If the set of values of p for which roots of the equation 2 x2-(2 p-3) x+2=0 are 2(-2/ sin -1 α) and 2(2/π) sin -1 α for some value of α in [-1,1] is [a, b], then 12(a+b) is (A) 30 (B) 50 (C) 90 (D) 100

Tardigrade Admin · Accepted Answer

For any value of α, product of the roots is 1 and sum of the roots lying in [2, (5/2)] ∴ 2 ≤ (2 p -3/2) ≤ (5/2) ⇒ 4 ≤ 2 p -3 ≤ 5 ⇒ p ∈[(7/2), 4]

Q. If the set of values of $p$ for which roots of the equation $2 x^{2} - (2 p - 3) x + 2 = 0$ are $2^{\frac{- 2}{s i n ^{- 1} α}}$ and $2^{\frac{2}{π} s i n^{- 1} α}$ for some value of $α$ in $[- 1, 1]$ is $[a, b]$ , then $12 (a + b)$ is

30

50

90

100

For any value of $α$ , product of the roots is 1 and sum of the roots lying in $[2, \frac{5}{2}]$
$∴ 2 \leq \frac{2 p - 3}{2} \leq \frac{5}{2} \Rightarrow 4 \leq 2 p - 3 \leq 5 \Rightarrow p \in [\frac{7}{2}, 4]$

Q. If the set of values of p for which roots of the equation 2x2−(2p−3)x+2=0 are 2sin−1α−2​ and 2π2​sin−1α for some value of α in [−1,1] is [a,b], then 12(a+b) is

30

50

90

100

For any value of α, product of the roots is 1 and sum of the roots lying in [2,25​] ∴2≤22p−3​≤25​⇒4≤2p−3≤5⇒p∈[27​,4]

Q. If the set of values of $p$ for which roots of the equation $2 x^{2} - (2 p - 3) x + 2 = 0$ are $2^{\frac{- 2}{s i n ^{- 1} α}}$ and $2^{\frac{2}{π} s i n^{- 1} α}$ for some value of $α$ in $[- 1, 1]$ is $[a, b]$ , then $12 (a + b)$ is

For any value of $α$ , product of the roots is 1 and sum of the roots lying in $[2, \frac{5}{2}]$
$∴ 2 \leq \frac{2 p - 3}{2} \leq \frac{5}{2} \Rightarrow 4 \leq 2 p - 3 \leq 5 \Rightarrow p \in [\frac{7}{2}, 4]$