If the discriminant of 5u2 + bu + 2 = 0 is 41, fi nd all values of b.
Maths
for 5u^2 + bu + 2 = 0
a = 5 , b = b and c = 2
b^2 - 4(5)(2) = 41
b^2 = 81
b = ± √81 = ±9
To find all values of b, we need to use the Quadratic Formula and solve for b using the given discriminant.
The quadratic formula is as follows:
For a quadratic equation ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, we have a quadratic equation 5u^2 + bu + 2 = 0, with a = 5, b = b, and c = 2.
We are given that the discriminant is 41, which is represented by (b^2 - 4ac).
Therefore, we can substitute these values into the quadratic formula:
(b^2 - 4ac) = 41
Substituting a = 5 and c = 2, we have:
b^2 - 4(5)(2) = 41
b^2 - 40 = 41
b^2 = 81
Taking the square root of both sides, we have:
b = ± √81
b = ± 9
Therefore, the values of b that satisfy the given condition are b = 9 and b = -9.