Question

Please solve this inequation​

Answer 1

Answer:

-20 is the solution.

Step-by-step explanation:

x+3=0

x= -3

put p(x) = -3

⇒ x²+6x-11

⇒ (-3)²+6(-3)-11

⇒ 9-18-11

⇒ -20

Answer 2

Solution:

$\boldsymbol{\dfrac{x^{2}+6x-11}{x+3} \: < \: -1}$

Adding 1 on both sides,

$\implies \sf{\dfrac{x^{2}+6x-11}{x+3}+1\: <\:0}$

On taking LCM,

$\dashrightarrow \: \: \sf{\dfrac{x^2+6x-11 + x + 3}{x+3}\:<\:0}$

$\implies \sf{\dfrac{x^{2}+7x-8}{x+3}\:<\:0}$

Now, Factorise the quadratic expression in numerator.

$\hookrightarrow \: \: \sf{\dfrac{x^2-x+8x-8}{x+3}\:<\:0}$

$\implies \sf{\dfrac{x(x-1)+8(x-1)}{x+3}<0}$

$\implies \sf{\dfrac{(x+8)(x-1)}{x+3}<0}$

Now, by  wavy curve method;

Consider the portion where the wave takes negative values as the above equation is lesser than 0.

(Refer to attachment)

$\therefore \boxed{\bf{x \in (- \infty, -8) \: \cup \: (-3,1)}}$