The values of p for which one root of the equation x2-(p+1) x+p2+p=8 exceeds 2 and the other is lesser than 2 are given by

Question

The values of p for which one root of the equation x2-(p+1) x+p2+p=8 exceeds 2 and the other is lesser than 2 are given by (A) 3< p < 10 (B) p ≤-2 (C) p ≥ 10 (D) -2< p < 3

Tardigrade Admin · Accepted Answer

x 2-( p +1) x + p 2+ p -8=0 f (2)<0 ⇒ 4-2( P +1)+ P 2+ P -8<0 ⇒ P 2- P -6<0 ⇒( P -3)( P -2)<0 ⇒ P ∈(-2,-3)

Q. The values of $p$ for which one root of the equation $x^{2} - (p + 1) x + p^{2} + p = 8$ exceeds 2 and the other is lesser than 2 are given by

$3 <$ p $< 10$

p $\leq - 2$

$p \geq 10$

$- 2 <$ p $< 3$

$x^{2} - (p + 1) x + p^{2} + p - 8 = 0$
$f (2) < 0$
$\Rightarrow 4 - 2 (P + 1) + P^{2} + P - 8 < 0$
$\Rightarrow P^{2} - P - 6 < 0 \Rightarrow (P - 3) (P - 2) < 0$
$\Rightarrow P \in (- 2, - 3)$

Q. The values of p for which one root of the equation x2−(p+1)x+p2+p=8 exceeds 2 and the other is lesser than 2 are given by

3< p <10

p ≤−2

p≥10

−2< p <3