Question

if the range of the expression (x^2+2x-11)/x-3 for real value of x is (-infinite, a] union [b, infinite) then a and b are​

Answer 1

Answer:

a = 4 and b=12

So the explanation is given in the above image . Thank you

Answer 2

Given:

(x²+2x-11)/x-3

To Find:

a and b

Solution:

y = $\frac{x^{2} +2x-11}{x-3}$     [(-∞,a)(b,∞)

x²+ 2x-11 = yx-3y

x² +(2- y)x - (11- 3y) =0

Now,

D ≥ 0

⇒ b² - 4ac > 0

⇒ (2-y)² - 4(3y -11) (1) ≥ 0

⇒ 4 + y² - 4y- 12y+44 ≥0

⇒ y²-16y +48 ≥ 0

⇒ (y-12)(y-4) ≥ 0

And when we put the equation on the number line we get,

(-∞,4)(12,∞)

a = 4 and b = 12

Therefore, the value of a is 4 and the value of b is 12.