Find all real zeros (estimate the irrational zeros to the nearest hundredth).
-$f ( x ) = x ^ { 4 } - 3 x ^ { 2 } - 10$
A)-2.24, 2.24
B)5, -1.41, 1.41
C)3.16, -5
D)10, 2.24

Question

Quizplus · Accepted Answer

The given function $f(x) = x^4 - 3x^2 - 10$ can be solved by substituting $y = x^2$, which turns the equation into a quadratic form $y^2 - 3y - 10 = 0$. Solving this quadratic equation gives $y = 5$ and $y = -2$. Since $y = x^2$, and $x^2$ cannot be negative, we discard $y = -2$ and only consider $y = 5$, which gives $x = \sqrt{5}$ and $x = -\sqrt{5}$. Estimating $\sqrt{5}$ to the nearest hundredth gives approximately 2.24. Therefore, the real zeros are -2.24 and 2.24.

Find All Real Zeros (Estimate the Irrational Zeros to the Nearest