Q. Use the quadratic formula to solve. Express your answer in simplest form.q2+10q+25=0Answer: q=
Quadratic Formula: The quadratic formula is given by q=2a−b±b2−4ac, where a, b, and c are the coefficients of the quadratic equationax2+bx+c=0. In this case, a=1, b=10, and c=25.
Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4ac. For our equation, the discriminant is 102−4(1)(25).
Discriminant Calculation: Calculating the discriminant: 102−4(1)(25)=100−100=0.
Apply Quadratic Formula: Since the discriminant is 0, the equation has one real root (a repeated root). We can now apply the quadratic formula with the discriminant: q=2a−b±(0).
Plug in Values: Plugging in the values of a and b into the formula: q=(2⋅1−10±(0)).
Simplify Expression: Simplifying the expression: q=2−10±0=2−10.
Final Solution: The final solution is q=−5. Since the discriminant was 0, this is the only solution.