Question

Richard is using an equation to plan out the dimensions of a new rectangular fence. The area within Richard's fence is given by the equation a = 2x² - 11x - 21. For which value would the area within the fence be equal to zero?

Answer 1

To find the value for which the area within the fence is equal to zero in the given quadratic equation, we can use the quadratic formula to solve it.

Step-by-step explanation:

To find the value for which the area within the fence is equal to zero, we need to solve the quadratic equation 2x² - 11x - 21 = 0. We can do this by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

Substituting the values from the equation a = 2, b = -11, and c = -21 into the formula, we get:

x = (-(-11) ± √((-11)² - 4(2)(-21)))/(2(2))

Simplifying further, we have:

x = (11 ± √(121 + 168))/(4)

x = (11 ± √(289))/(4)

Now we can calculate the two possible values for x:

x = (11 ± 17)/(4)

Therefore, the two possible values for x that would make the area within the fence equal to zero are x = 7/2 or x = -3.