Wielomian $w$ określony jest wzorem:

$w\left(x\right)=-2x^4+a{x}^2+2x-4$

Wiemy, że $w\left(\sqrt{2}\right)=-w\left(-\sqrt{2}\right)$.

$w\left(\sqrt{2}\right)=-2\cdot {\left(\sqrt{2}\right)}^4+a\cdot {\left(\sqrt{2}\right)}^2+2\cdot \sqrt{2}-4=$

$=-2\cdot 4+a\cdot 2+2\sqrt{2}-4=-12+2a+2\sqrt{2}$

$-w\left(-\sqrt{2}\right)=-\left(-2\cdot {\left(-\sqrt{2}\right)}^4+a\cdot {\left(-\sqrt{2}\right)}^2+2\cdot \left(-\sqrt{2}\right)-4\right)=$

$=-\left(-2\cdot 4+a\cdot 2-2\sqrt{2}-4\right)=-\left(-8+2a-2\sqrt{2}-4\right)=$

$=-\left(-12+2a-2\sqrt{2}\right)=12-2a+2\sqrt{2}$

Zapisujemy równanie:

$-12+2a+2\sqrt{2}=12-2a+2\sqrt{2}$

$4a=24|:4$

$a=6$

Odp. A