Question

If one zero of polynomial p (x) =x2-6x+k is twice the other than find the value of k

Answer 1

Answer:

k= 2

Step-by-step explanation:

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Answer 2

Answer:

If one zero of polynomial p (x) =x2-6x+k is twice the other than find the value of k is 8

Step-by-step explanation:

Step 1: Consider the equation x^2-6 x+q=0, where a=1, b=-6, c=q

(i) Sum of the roots $m+n=\frac{-b}{a}=\frac{-(-6)}{1} \therefore m+n=6$

(ii) Product of the roots $\mathrm{mn}=\frac{\mathrm{c}}{\mathrm{a}}=\frac{\mathrm{q}}{1} \therefore \mathrm{mn}=\mathrm{q}$

Step 2: If one root is $\mathrm{m}$ then twice the root is $2 \mathrm{~m}$.

$\therefore m=m$ and n=2 m

$\mathrm{m}+\mathrm{n}=6 \therefore \mathrm{m}+2 \mathrm{~m}=6,3 \mathrm{~m}=6 \therefore \mathrm{m}=\frac{6}{3}=2$

Step 3: We know that $\mathrm{q}=\mathrm{mn} \therefore \mathrm{q}=\mathrm{m}(2 \mathrm{~m})=2 \mathrm{~m}^2=2(2)^2=8 \therefore \mathrm{q}=8$

q=k=8.

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