d. \( -5 x^{2}+4 x-1

Ask by Thornton Kelly. in Norway

Dec 10,2024

To solve the inequality \(-5x^{2}+4x-1 < x^{2}-3x-4\), first, let's bring all terms to one side to combine like terms, yielding: \[ -5x^{2} - x^{2} + 4x + 3x - 1 + 4 < 0 \] Simplifying this results in: \[ -6x^{2} + 7x + 3 < 0 \] Now, you can factor the left-hand side or use the quadratic formula to find the roots. Once the roots are computed, testing intervals between the roots helps determine where the quadratic is negative. While solving inequalities, always remember to check if you've flipped the inequality sign—this typically happens if you're multiplying or dividing by a negative number. Happy solving!