Question

k is a zero of polynomial p x is equal to x square - 11 x + 24 if K is a prime number then find the value of k ​

Answer 1

Given

$\sf{p(x) = x {}^{2} - 11x + 24 }$

To find:

Value of K which is a zero of the given polynomial

Remainder Theorem

$\sf{p(x) = 0}$

Thus,

$\sf{x {}^{2} - 11x + 24 = 0} \\ \\ \rightarrow \: \sf{x {}^{2} - 8x - 3x + 24 = 0 } \\ \\ \rightarrow \: \sf{x(x - 8) - 3(x - 8) = 0} \\ \\ \rightarrow \: \sf{(x - 8)(x - 3) = 0} \\ \\ \rightarrow \: \underline{\boxed{\sf{x = 3 \: or \: 8}}}$

Thus,the zeros of the given polynomial are 3 and 8

Now,

K is a prime number

$\implies \: \boxed{ \boxed{ \sf{k = 3}}}$