1. Tardigrade
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  3. Mathematics
  4. 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

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

Complex Numbers and Quadratic Equations

Solution:

$ 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 $=2$