What are the two roots for the equation x^2 + 7x + 10 = 0

Start by looking for multiples of 10. You have the pairs 2 & 5 and 1 & 10. Both signs are positive in the original equation so it will either be positive 2 & 5 or positive 1 & 10. Clearly 2+5=7 therefore we get (x+5)(x+2)=0. In order to satisfy the equation the values of x must be x=-5 and x=-2