If A and B are the roots of the equations 2xx -11× +5=0,find the value of
1) A-B
To find the value of A-B, we need to first find the values of A and B.
Given the quadratic equation 2xx -11× +5=0, we can find the roots by using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 2, b = -11, and c = 5.
Using the quadratic formula, we can find the values of A and B:
For A:
x = (-(-11) ± √((-11)^2 - 4(2)(5)))/(2(2))
= (11 ± √(121 - 40))/4
= (11 ± √81)/4
= (11 ± 9)/4
This gives two possible values for A:
A = (11 + 9)/4 = 5
A = (11 - 9)/4 = 1/2
For B:
x = (-(-11) ± √((-11)^2 - 4(2)(5)))/(2(2))
= (11 ± √(121 - 40))/4
= (11 ± √81)/4
= (11 ± 9)/4
This gives two possible values for B:
B = (11 + 9)/4 = 5
B = (11 - 9)/4 = 1/2
So A and B both have the possible values of 5 and 1/2.
To find A-B, we subtract the values of B from the values of A:
When A = 5 and B = 5:
A - B = 5 - 5 = 0
When A = 5 and B = 1/2:
A - B = 5 - (1/2) = 9/2
When A = 1/2 and B = 5:
A - B = (1/2) - 5 = -9/2
When A = 1/2 and B = 1/2:
A - B = (1/2) - (1/2) = 0
Therefore, the possible values of A-B are 0 and 9/2.