Question

19. Obtain all the zeros of the polynomial x4 + x - 14x2 – 2x + 24 if two of
its zeros are ,√2 and -√2.​

Answer 1

Answer:

Step-by-step explanation:

p(x) = $x^{4}$ + $x^{3}$ - $14x^{2}$- 2x + 24

here

(x-$\sqrt{2}$)(x+$\sqrt{2}$) are the factors of p(x)

= $x^{2}$-4 is a factor of p(x)      [(a-b)(a+b) = $a^{2}$ -$b^{2}$]

$\sqrt[x^{2}-4 ]{x^{4}+x^{3}- 14x^{2}-2x^{1} +24 }$

on dividing the whole eq we get the quotient as $x^{2}$+x-10

on factorising