Final answer:
The maximum root of a quadratic equation can be calculated using the quadratic formula. Substituting the values of the equation into the formula will yield the maximum root. The correct answer is b) (-b+√(b²-4ac))/(2a).
Step-by-step explanation:
The maximum root of a quadratic equation in standard form ax²+bx+c = 0 is found using the quadratic formula with the plus sign, which is (-b+√(b²-4ac))/(2a).
The maximum root of a quadratic equation can be calculated using the quadratic formula. The quadratic formula is:
x = (-b ± √(b²-4ac))/(2a)
Where a, b, and c are the coefficients of the quadratic equation ax²+bx+c=0.
For example, let's say we have the quadratic equation 2x²+5x-3=0. By substituting the values a=2, b=5, and c=-3 into the equation, we get:
x = (-5 ± √(5²-4(2)(-3)))/(2(2))
This simplifies to:
x = (-5 ± √(25+24))/(4)
Which further simplifies to:
x = (-5 ± √(49))/(4)
So, the maximum root of this quadratic equation is:
x = (-5 + 7)/(4) = 1