The zero of a polynomial function is a number a such as h(a)=0.
For quadratic equation, the zeros can be found on equalizing h to 0.
First, h(x+5)=(x+5)²+3(x+5)-10=x²+10x+25+3x+15-10=x²+13x+30, and it is said that if h(x+5)=x^2+kx+30 = x²+13x+30, it implies k=13, so to find the zeros...
x²+13x+30=0 is to solve: D=13²-4x1x30=169-120=49, sqrt 49=7, so x=-13-7 / 2=-20/2 = -10, and x= -13+7/ 2 = -6 /2= -3.
We know that -10< -3, so the smallest zero is -10.