Final answer:
The values of 'b' that will cause the quadratic equation 4x² + bx + 25 = 0 to have one real solution are b = -20 and b = 20.
Step-by-step explanation:
A quadratic equation of the form at² + bt + c = 0 has one real solution if and only if the discriminant, b² - 4ac, equals zero. In this case, the given equation is 4x² + bx + 25 = 0. Comparing this equation with the general form, we have a = 4, b = b, and c = 25. Therefore, for one real solution, we need the discriminant to be zero:
b² - 4ac = 0
Substituting the values, we get:
b² - 4(4)(25) = 0
Simplifying further, we have:
b² - 400 = 0
Adding 400 to both sides, we get:
b² = 400
Taking the square root of both sides, we get:
b = ±20
Therefore, the values of 'b' that will cause the quadratic equation to have one real solution are b = -20 and b = 20.