Step-by-step explanation:

The given Polynomial is

(K²-14)x²-2x-12

Therefore,a=(K²-14),b=-2,c=-12

The sum of zeroes of a quadratic poly =-(-2)/k²-14

2/k²-14=1

2=1(k²-14)

2=k²-14

K²=+2+14

K²=16

K=√16

K=4

Verified answer

Polynomial:-

[tex] = > \blue{( {k}^{2} - 14) {x}^{2} - 2x - 12}[/tex]

To Find:-

[tex] = > \red{ value \: of \: k}[/tex]

Solution:-

[tex] \bf ✎sum \: of \: zeroes = \frac{ -b }{a} [/tex]

[tex] \orange{∴1 = \frac{ - ( - 2)}{ {k}^{2} - 14 } }[/tex]

[tex]1 = \frac{2}{ {k}^{2} - 14 } [/tex]

[tex] {k}^{2} - 14 = 2 \\ {k}^{2} = 14 + 2 \\ {k}^{2} = 16 \\ = > \color{cyan} \boxed{k = \frac{ + }{ } 4}[/tex]

So,

Value of k is ± 4