Answers: k = 13The smallest zero or root is x = -10 =============================== Work Shown: note: you can write "x^2" to mean "x squared" f(x) = x^2+3x-10 f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5 f(x+5) = (x^2+10x+25)+3(x+5)-10 f(x+5) = x^2+10x+25+3x+15-10 f(x+5) = x^2+13x+30 Compare this with x^2+kx+30 and we see that k = 13 Factor and solve the equation below x^2+13x+30 = 0 (x+10)(x+3) = 0 x+10 = 0 or x+3 = 0 x = -10 or x = -3 The smallest zero is x = -10 as its the left-most value on a number line.
