Question

K is a zeroes of polynomial p (x)=x^2-11x+24if k is a prime number find value of k

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 = 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

Hey fab ,

The polynomial is :-
${x}^{2} - 11x + 24 = 0$

Let's factorise it ,
$= > {x}^{2} - 8x - 3x + 24 = 0$
$= > x(x - 8) - 3(x - 8) = 0$
$= > (x - 8)(x - 3) = 0$
So ,
x = 8 and 3 .
And here 3 is prime number .
So , k = 3 .


Complicated Life :(