The equation \( x^{2}+5 x-17=0 \) has two solutions \( A \) and \( B \) where \( A

Ask by Washington Bates. in the United States

Jan 23,2025

To solve for \( A \) and \( B \), we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a=1 \), \( b=5 \), and \( c=-17 \). Plugging in these values, we find the discriminant \( b^2 - 4ac = 5^2 - 4(1)(-17) = 25 + 68 = 93 \). Thus, the two solutions are: \[ x = \frac{-5 \pm \sqrt{93}}{2} \] Calculating the approximate values, we find \( A \approx -8.3 \) and \( B \approx 3.3 \). Finding the roots of quadratic equations isn't just a classroom exercise; it has real-life applications! For instance, engineers use these types of equations to determine optimal dimensions for structures, where the area or volume is maximized or minimized—much like how your favorite pizza places ensure they give you the most delicious slice possible, calculated to perfection! A common mistake in solving these equations is skipping over the step of checking the discriminant. If the discriminant is negative, the solutions become complex numbers, which may trip you up if you're expecting real solutions. Always take a moment to calculate that discriminant first; it'll save you from surprises and keep those math mistakes at bay!