The possible set of values of a for which one root of equation x2+2(a-1) x+a+5=0 is smaller than 1 and other root is greater than 3 is

Question

The possible set of values of a for which one root of equation x2+2(a-1) x+a+5=0 is smaller than 1 and other root is greater than 3 is (A) ((-4/3), (-8/7)) (B) (-∞, (-8/7)) (C) (-∞, (-4/3)) (D) ((8/7), ∞)

Tardigrade Admin · Accepted Answer

f (1) < 0 and f(3) < 0 a ∈(-∞, (-4/3))

Q. The possible set of values of a for which one root of equation $x^{2} + 2 (a - 1) x + a + 5 = 0$ is smaller than 1 and other root is greater than 3 is

$(\frac{- 4}{3}, \frac{- 8}{7})$

$(- \infty, \frac{- 8}{7})$

$(- \infty, \frac{- 4}{3})$

$(\frac{8}{7}, \infty)$

$f (1) < 0$ and $f (3) < 0$
$a \in (- \infty, \frac{- 4}{3})$

Q. The possible set of values of a for which one root of equation x2+2(a−1)x+a+5=0 is smaller than 1 and other root is greater than 3 is

(3−4​,7−8​)

(−∞,7−8​)

(−∞,3−4​)

(78​,∞)