1. **Problem**: Find the zeros of the quadratic polynomial $P(x) = x^2 + 7x + 10$ and verify the relationship between the zeros and coefficients. 2. **Identify the polynomial**: Given $P(x) = x^2 + 7x + 10$. 3. **Find zeros by factorization**: To solve $x^2 + 7x + 10 = 0$, We look for two numbers that multiply to $10$ (constant term) and add to $7$ (coefficient of $x$). 4. These numbers are $2$ and $5$, so we factorize as: $$x^2 + 7x + 10 = (x + 2)(x + 5) = 0$$ 5. **Find zeros**: Set each factor equal to zero: $$x + 2 = 0 \implies x = -2$$ $$x + 5 = 0 \implies x = -5$$ 6. **Verify relationship between zeros and coefficients**: - Sum of zeros $= -2 + (-5) = -7$, which should equal $-\frac{b}{a} = -\frac{7}{1} = -7$. - Product of zeros $= (-2) \times (-5) = 10$, which should equal $\frac{c}{a} = \frac{10}{1} = 10$. 7. **Conclusion**: The zeros $-2$ and $-5$ satisfy the relationships with coefficients as expected. **Final answer:** Zeros are $x = -2$ and $x = -5$, verified with sum and product relationships.