Question

If one zero of 14² − 42² − 9 is the negative of the other, find the value of k �

Answer 1

Given

One of the zeros of 14² − 42² − 9 is the negative of the other.

To find the value of k.

Step-by-step explanation:

It is given that,

One of the zeros of 14² − 42² − 9 is the negative of the other.

That implies,

Let α, -α be the zeros of the polynomial f(x) = 14² − 42² − 9.

Then,

`\begin{gathered} f(\alpha)=0 \\ \Rightarrow14\alpha^2-42k^2\alpha-9=0\text{ \_\_\_\_\_\_\lparen1\rparen} \end{gathered}`

Also,

`\begin{gathered} f(-\alpha)=0 \\ \Rightarrow14\alpha^2+42k^2\alpha-9=0\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}`

Subtracting (1) and (2) implies,

`\begin{gathered} (2)-(1)\Rightarrow(14\alpha^2+42k^2\alpha-9)-(14\alpha^2-42k^2\alpha-9)=0 \\ \Rightarrow84k^2\alpha=0 \\ \Rightarrow k^2\alpha=0 \\ \because\alpha\\e0\Rightarrow k^2=0 \\ \Rightarrow k=0 \end{gathered}`

Hence, the value of k is 0.