Flashcard 8 - Mathematics Knowledge Flashcard Set for the ASVAB

Solve for the value of \(x\) when \(x^2 - 11x + 30 = 0\).

When a question asks about the zeroes or roots of a polynomial, it’s the same as “solving the polynomial” or “solving for the value of x” when the polynomial is equal to zero. Proceed by factoring the polynomial and equating each factor to zero. The zeroes of this polynomial are: \(x = 5\) and \(x = 6\). Here’s how this process would look:

\[x^{2} - 11x + 30 = 0\] \[(x - 5)(x - 6) = 0\] \[x - 5 = 0 \;\text{and} \;x - 6 = 0\] \[x = 5\; \text{and} \;x = 6\]