Each expression is a perfect square. assuming b is greater than 0, find b.
A. y=x^2+bx+49
B. y=x^2+bx+1
To find the value of "b" when each expression is a perfect square, we need to factor each expression into a perfect square form.
A. y = x^2 + bx + 49
In order for this expression to be a perfect square, it needs to be in the form of (x + c)^2 for some constant 'c'. We can expand (x + c)^2 to get x^2 + 2cx + c^2.
Comparing this to the given expression y = x^2 + bx + 49, we can see that 2c = b, and c^2 = 49.
Since 'c' is a constant and b is greater than 0 (as given), the only possible value for b is 2c. Similarly, the only possible value for 'c' is the positive square root of 49, which is 7.
Therefore, b = 2c = 2 * 7 = 14.
B. y = x^2 + bx + 1
Using the same approach, this expression needs to be in the form of (x + c)^2.
Expanding (x + c)^2 gives us x^2 + 2cx + c^2.
Comparing this to the given expression y = x^2 + bx + 1, we have 2c = b and c^2 = 1.
Since 'c' is a constant and 'b' is greater than 0, the only possible value for b is 2c. Similarly, the only possible value for 'c' is the positive square root of 1, which is 1.
Therefore, b = 2c = 2 * 1 = 2.
In summary, the value of 'b' is 14 for expression A, and 'b' is 2 for expression B.