Question

pls solve this question

Answer 1

Hope it helps buddy

Answer 2

Answer:

√2, - √2, 3, -4

Step-by-step explanation:

Let p(x) = x⁴ + x³ - 14x² - 2x + 24.

Given Zeroes are √2 and -√2.

Hence, (x + √2)(x - √2) is a factor.

= (x² - 2).

Now,

Dividing the polynomial by (x² - 2)

We can find out the factors.

x² - 3) x⁴ + x³ - 14x² - 2x + 24 (x² + x - 12

         x⁴         - 2x²

         --------------------------------

                 x³ - 12x² - 2x + 24

                 x³           - 2x

          ----------------------------------

                        -12x²         + 24

                        -12x²         + 24

           --------------------------------

                                       0

Now,

Factorize x² + x - 12

x² + x - 12 = 0

x² + 4x - 3x - 12 = 0

x(x + 4) - 3(x + 4) = 0

(x - 3)(x + 4) = 0

x = 3, -4.

Therefore, the zeroes of the polynomial are √2, -√2, 3, -4.

Hope it helps!