what substitution should be used to rewrite $4x^{12}-5x^{6}-14 = 0$ as a quadratic equation?\n$u =…
what substitution should be used to rewrite $4x^{12}-5x^{6}-14 = 0$ as a quadratic equation?\n$u = x^{2}$\n$u = x^{3}$\n$u = x^{6}$\n$u = x^{12}$
Answer
Answer:
C. $u = x^{6}$
Explanation:
Step1: Recall exponent rule
$(a^{m})^{n}=a^{mn}$. So $x^{12}=(x^{6})^{2}$.
Step2: Substitute $u = x^{6}$
The equation $4x^{12}-5x^{6}-14 = 0$ becomes $4u^{2}-5u - 14=0$, which is a quadratic equation in terms of $u$.