Final answer:
To find the largest value of x that solves the quadratic equation, x² - 4x - 3 = 0, we can use the quadratic formula. The largest value of x is (4 + sqrt(28)) / 2. The correct answer is b) 2.
Step-by-step explanation:
To find the largest value of x that solves the equation x² - 4x - 3 = 0, we can use the quadratic formula. The formula is x = (-b ± sqrt(b² - 4ac)) / (2a), where a = 1, b = -4, and c = -3. Plugging in these values, we get x = (-(-4) ± sqrt((-4)² - 4(1)(-3))) / (2(1)).
Simplifying further, we have x = (4 ± sqrt(16 + 12)) / 2. This gives us two possible values for x: x = (4 ± sqrt(28)) / 2. The largest value of x is obtained when we take the positive square root, so the answer is x = (4 + sqrt(28)) / 2.
An equation is a mathematical statement asserting that two expressions are equal. It contains an equal sign ("=") separating the left-hand side (LHS) and the right-hand side (RHS). The goal in solving an equation is to find the value(s) of the variable(s) that satisfy the equality.