If α and β are roots of x^2+px+q=0 and α+1 and β+1 are roots of x^2-5x+6=0, what are p and q?

p=-3, q=2

The equation x^2-5x+6=0 has roots 2 and 3, since it factors as (x-2)(x-3). Therefore α+1 and β+1 are 2 and 3, so α and β are 1 and 2. Their sum is α+β=3 and their product is αβ=2. For x^2+px+q=0, Vieta’s relations give α+β=-p and αβ=q. Thus -p=3, giving p=-3, and q=2. Hence option A is correct. Alternatively, shifting the known roots backward by 1 directly gives the polynomial (x-1)(x-2)=x^2-3x+2, which has the form x^2+px+q. The other options have an incorrect sign or interchange the required parameter values.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.