Question

If the zeros of polynomial x square - 8 x + k is equal to zero are the HCF of (6 12), then find the value of k

Answer 1

The value of k in the given polynomial $x^2-8x+k=0$ is 12

∴ k=12

Step-by-step explanation:

Given polynomial is $x^2-8x+k=0$

Also given that the zeros of the given polynomial is the HCF of 6 and 12

HCF of 6=2,3,6 and 12=2,3,6,12

Therefore the HCF of 6 and 12 is 6

Therefore 6 is the zero of the given polynomial

We can write it as x-6=0

x=6

Now To find the value of k :

• Put x=6 in the given polynomial $x^2-8x+k=0$
• $6^2-8(6)+k=0$
• $36-48+k=0$
• $-12+k=0$
• $12+k+12=0+12$
• $k=12$

The value of k in the given polynomial is 12

∴ k=12