Question

If the sum of the zeros of the polynomial
P(x) = (k²-14) x² - 2x - 4 is 1 find values k. ​

Answer 1

$P(x)=( {k}^{2} -14) {x }^2- 2x - 4 =0\\</p><p>P(1)=( {k}^{2} -14)({1})^2-2(1)-4=0\\⇒( {k}^{2} -14)1-2-4=0 \: \\⇒ {k}^{2} -14-6=0\\</p><p>⇒ {k}^{2} -20=0\\⇒ {k}^{2} =20\\⇒k= \sqrt{20} \\⇒$