Let r and s be the roots of y^2 - 19y + 7. Find (r-2)*(s-2).
r-2 and s-2 are the roots of
(y+2)^2 - 19(y+2) + 7 = 0
y^2 - 15y - 27 = 0
The product of the roots of the shifted function is -27
To find the value of (r-2)*(s-2), we need to first find the roots of the given quadratic equation y^2 - 19y + 7.
The quadratic equation y^2 - 19y + 7 can be factored as (y - r)(y - s) = 0, where r and s are the roots.
To factorize the quadratic equation, we need to find two numbers that multiply to give 7, and add up to give -19. By analyzing the factors of 7, we find that 1 and 7 satisfy these conditions. So the factored form of the quadratic equation is:
(y - r)(y - s) = (y - 1)(y - 7) = 0.
From this equation, we can see that the roots are r = 1 and s = 7.
Now, let's substitute these values into the expression (r-2)*(s-2):
(r-2)*(s-2) = (1-2)*(7-2) = (-1)*(5) = -5.
Therefore, the value of (r-2)*(s-2) is -5.