Question

K is a zero of the polynomial p(x)=x²-11x+24 if k is a prime numbers then find the value of k.
Please answer it fast!!

Answer 1

Hey 

Given polynomial is :- 
p ( x ) = x² - 11x + 24 
K is it's one of the zero . 

So , let's find the zeros if this polynomial to find the value of k . 

x² - 11x + 24 = 0 
D = ( -11 ) ² - 4 * 1 * 24
D = 121 - 96 
D = 25 

So 
\sqrt{d} = \sqrt{25}d​=25​ 

d = 5 

Now , 
x = -b ±√D /2a 
x = -( -11 ) + 5 / 2
x = 11 + 5 / 2
x = 16 / 2
x = 8 . 

And , 
x = -(-11) - 5 / 2
x = 11 -5 /2
x = 6 / 2
x = 3 . 

Here 3 is prime number . 
So , k = 3 . 

thanks :) 

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Answer 2

Given :

p ( x ) = x² - 11 x + 24

What is a zero ?

A zero is the value of x for which p ( x ) = 0

So :

p ( x ) = 0 ==> x² - 11 x + 24 = 0

x² - 8 x - 3 x + 24 = 0

==> x ( x - 8 ) - 3 ( x - 8 ) = 0

==> ( x - 3 )( x - 8 ) = 0

Either

x - 3 = 0

==> x = 3

or

x - 8 = 0

==> x = 8

The only prime zero is 3

So the value of k is 3

Hope it helps

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