Question

Para quais valores de a e b o polinômio p(x) = (a^2 - 9)x^4 + (2b + 1)x^2 é nulo?

Answer 1

O polinômio nulo possui todos os coeficientes nulos. Ou seja:

$q(x)=0=0x^{n}+0x^{n-1}+...+0x+0$
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$p(x)=(a^{2}-9)x^{4}+(2x+1)x^{2}$

Para p(x) ser nulo, devemos ter:

$a^{2}-9=0~~~\therefore~~~a^{2}=9~~~\therefore~~~\sqrt{a^{2}}=\sqrt{9}~~~\therefore~~~|a|=3~~~\therefore~~~\boxed{\boxed{a=\pm3}}$

e:

$2b+1=0~~~\therefore~~~2b=-1~~~\therefore~~~\boxed{\boxed{b=-\dfrac{1}{2}}}$