Q.According to the rational root theorem, which number is not possible rational zero of $4x^7+2x^4-10x^3-5$?

Step 1. List the Rational Root Theorem's constraints. For $4x^7+2x^4-10x^3-5=0$: any rational root $p/q$ (lowest terms) needs $p\mid5$ (so $p\in\{\pm1,\pm5\}$) and $q\mid4$ (so $q\in\{\pm1,\pm2,\pm4\}$).

Step 2. Test option (1), $-1$. $p=1,q=1$: both valid divisors — possible.

Step 3. Test option (2), $\tfrac54$. $p=5,q=4$: both valid divisors — possible. …

Rational Root Theorem — check each option's numerator against the divisors of $a_0$ and den …

• Mixing up which of $p,q$ must divide $a_0$ vs $a_n$
• Assuming any 'reasonable-looking' fraction is automaticall …