If α, β are roots of 2 x2-5 x+p=0, such that 0

Question

If α, β are roots of 2 x2-5 x+p=0, such that 0<α<1 and 1<β<3, then the number of integral values of p is (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

f (0)>0 ⇒ p >0 ....(1) f (1)<0 ⇒ 2-5+ p <0 ⇒ (1) ....(2) f (3)>0 ⇒ 18-15+ p >0 ⇒ p >-3....(3) Intersection of (1), (2) and (3) p ∈(0,3) Number of integral values =2

Q. If $α, β$ are roots of $2 x^{2} - 5 x + p = 0$ , such that $0 < α < 1$ and $1 < β < 3$ , then the number of integral values of $p$ is

0

1

2

3

$f (0) > 0 \Rightarrow p > 0$ ....(1)
$f (1) < 0 \Rightarrow 2 - 5 + p < 0 \Rightarrow (1)$ ....(2)
$f (3) > 0 \Rightarrow 18 - 15 + p > 0 \Rightarrow p > - 3$ ....(3)
Intersection of (1), (2) and (3)
$p \in (0, 3)$
Number of integral values $= 2$

Q. If α,β are roots of 2x2−5x+p=0, such that 0<α<1 and 1<β<3, then the number of integral values of p is

0

1

2

3

f(0)>0⇒p>0 ....(1) f(1)<0⇒2−5+p<0⇒(1)....(2) f(3)>0⇒18−15+p>0⇒p>−3....(3) Intersection of (1), (2) and (3) p∈(0,3) Number of integral values =2

Q. If $α, β$ are roots of $2 x^{2} - 5 x + p = 0$ , such that $0 < α < 1$ and $1 < β < 3$ , then the number of integral values of $p$ is

$f (0) > 0 \Rightarrow p > 0$ ....(1)
$f (1) < 0 \Rightarrow 2 - 5 + p < 0 \Rightarrow (1)$ ....(2)
$f (3) > 0 \Rightarrow 18 - 15 + p > 0 \Rightarrow p > - 3$ ....(3)
Intersection of (1), (2) and (3)
$p \in (0, 3)$
Number of integral values $= 2$