Let α, β are roots of the equation (t-t2) x2-(1-t) x+t2=0 for any real number t belonging to (0, (1/2)) than

Question

Let α, β are roots of the equation (t-t2) x2-(1-t) x+t2=0 for any real number t belonging to (0, (1/2)) than (A) α and β are always imaginary ∀ t ∈(0, (1/2)) (B) for infinitely many values of t, corresponding root α is rational and for infinitely many values of 1 corresponding root α is irrational (C) α and β are real and positive such that one root is greater than 1 and other is smaller than 1 (D)  displaystyle lim t arrow (1-/2)|α-β|=0

Tardigrade Admin · Accepted Answer

Correct answer is (b) for infinitely many values of t, corresponding root α is rational and for infinitely many values of 1 corresponding root α is irrationalCorrect answer is (c) α and β are real and positive such that one root is greater than 1 and other is smaller than 1Correct answer is (d) displaystyle lim t arrow (1-/2)|α-β|=0

Q. Let $α, β$ are roots of the equation $(t - t^{2}) x^{2} - (1 - t) x + t^{2} = 0$ for any real number $t$ belonging to $(0, \frac{1}{2})$ than

$α$ and $β$ are always imaginary $\forall t \in (0, \frac{1}{2})$

for infinitely many values of t, corresponding root $α$ is rational and for infinitely many values of 1 corresponding root $α$ is irrational

$α$ and $β$ are real and positive such that one root is greater than 1 and other is smaller than 1

$t \to \frac{1 ^{-}}{2} lim ∣ α - β ∣ = 0$

Q. Let α,β are roots of the equation (t−t2)x2−(1−t)x+t2=0 for any real number t belonging to (0,21​) than

α and β are always imaginary ∀t∈(0,21​)

for infinitely many values of t, corresponding root α is rational and for infinitely many values of 1 corresponding root α is irrational

α and β are real and positive such that one root is greater than 1 and other is smaller than 1

t→21−​lim​∣α−β∣=0

Q. Let $α, β$ are roots of the equation $(t - t^{2}) x^{2} - (1 - t) x + t^{2} = 0$ for any real number $t$ belonging to $(0, \frac{1}{2})$ than

$α$ and $β$ are always imaginary $\forall t \in (0, \frac{1}{2})$

for infinitely many values of t, corresponding root $α$ is rational and for infinitely many values of 1 corresponding root $α$ is irrational

$α$ and $β$ are real and positive such that one root is greater than 1 and other is smaller than 1

$t \to \frac{1 ^{-}}{2} lim ∣ α - β ∣ = 0$