The real values of ' a ' for which the quadratic equation 2 x2-(a3+8 a-1) x+a2-4 a=0 possess roots of opposite sign is given by:

Question

The real values of ' a ' for which the quadratic equation 2 x2-(a3+8 a-1) x+a2-4 a=0 possess roots of opposite sign is given by: (A) a >5 (B) 0< a< 4 (C) a > 0 (D) a > 7

Tardigrade Admin · Accepted Answer

2 x2-(a3+8 a-1) x+(a2-4 a)=0 Since the roots are of opposite sign. f(0)< 0 ⇒ a2-4 a< 0 ⇒ a(a-4)< 0 ⇒ a ∈(0,4)

Q. The real values of ' $a$ ' for which the quadratic equation $2 x^{2} - (a^{3} + 8 a - 1) x + a^{2} - 4 a = 0$ possess roots of opposite sign is given by:

$a > 5$

$0 < a < 4$

$a > 0$

$a > 7$

$2 x^{2} - (a^{3} + 8 a - 1) x + (a^{2} - 4 a) = 0$
Since the roots are of opposite sign.
$f (0) < 0$
$\Rightarrow a^{2} - 4 a < 0$
$\Rightarrow a (a - 4) < 0$
$\Rightarrow a \in (0, 4)$

Q. The real values of ' a ' for which the quadratic equation 2x2−(a3+8a−1)x+a2−4a=0 possess roots of opposite sign is given by:

a>5

0<a<4

a>0

a>7