If α and β are the roots of the equation x^2+αx+β=0 such that α≠β, then the number of integral values of x satisfying x-β-α

Question

If α and β are the roots of the equation x^2+αx+β=0 such that α≠β, then the number of integral values of x satisfying x-β-α<1 is

MARKS Content Team · Accepted Answer

Correct answer: (C) 2. α,β are roots of x^2+αx+β=0 ⇒α+β=-α and αβ=β⇒α=1,β=-2 Now, x+2-1<1 ⇒-1<x+2-1<1 ⇒0<x+2<2 ⇒-2<x+2<2, x+2≠0 ⇒-4<x<0, x≠-2 ⇒x∈-4,-2∪-2,0 So, there are two integral values of x, i.e. -3,-1

If $α$ and $β$ are the roots of the equation $x^{2} + α x + β = 0$ such that $α \neq β$ , then the number of integral values of $x$ satisfying $||x - β| - α| < 1$ is

Solution

More Quadratic Equation Questions

If α and β are the roots of the equation x2+αx+β=0 such that α≠β, then the number of integral values of x satisfying x-β-α<1 is

Solution

More Quadratic Equation Questions

If $α$ and $β$ are the roots of the equation $x^{2} + α x + β = 0$ such that $α \neq β$ , then the number of integral values of $x$ satisfying $||x - β| - α| < 1$ is