Question

Find the range of the function. Kindly show steps

Answer 1

Answer:

x4 – 14x2 + 24x – k = 0 has four real and unequal roots .

Step-by-step explanation:

Let f(x) = x4 – 14x2 + 24x – k Then f'(x) = 4x3 – 28x + 24 = 4(x3 – 7x + 6) = 4(x – 1)(x – 2)(x + 3) So, f(x) = 0 has four unequal roots.

Now, f(– 3) = –117 – k,

f (1) = 11 – k and f(2) = 8 – k

By the sign scheme, f(1) < 0,

f(2) > 0 & f(– 3) < 0 ⇒ (8 – k) < 0,

11 – k > 0 & – 117 – k < 0 ⇒ k > 8,

k < 11 and k > – 117 ⇒ 8 < k < 11 Therfore, 8 < k

I hope it's helpful