Q. Use the quadratic formula to solve. Express your answer in simplest form.a2+4a+4=0a=□
Quadratic Formula Explanation: The quadratic formula is given by x=2a−b±b2−4ac, where ax2+bx+c=0. We will use this formula to find the roots of the given quadratic equationa2+4a+4=0.
Identify Coefficients: First, identify the coefficients a, b, and c from the quadratic equation. In this case, a=1, b=4, and c=4.
Calculate Discriminant: Next, calculate the discriminant, which is b2−4ac. For our equation, the discriminant is 42−4(1)(4)=16−16=0.
Apply Quadratic Formula: Since the discriminant is 0, there is only one real root, which is also called a repeated root. We can now apply the quadratic formula with the discriminant.
Substitute and Simplify: Substitute a, b, and c into the quadratic formula: a=2×1−4±0=2−4±0.
Final Answer: Simplify the expression: a=(−4)/2=−2.
Final Answer: Simplify the expression: a=(−4)/2=−2.The final answer is that the quadratic equation a2+4a+4=0 has one repeated root, which is a=−2.