Answer :
Answer:
k = 13 ;
The smallest zero is x = -10
Step-by-step explanation:
[tex]f(x) = x^2+3x-10[/tex]
Where;
[tex]x = x+5[/tex]
So;
[tex]f(x+5) = (x+5)^2+3(x+5)-10[/tex]
[tex]f(x+5) = x^2+10x+25+3x+15-10[/tex]
[tex]f(x+5) = x^2+13x+30[/tex]
We all know that : [tex]x^2+kx+30[/tex]
where k is synonymous with 13
[tex]x^2+13x+30 = 0[/tex]
solving this quadratic equation ; we have;
[tex](x+10)(x+3) = 0[/tex]
[tex]x+10 = 0\ \ \ or \ \ \ x+3 = 0[/tex]
[tex]x = -10 \ \ \ or \ \ \ x = -3[/tex]
Hence; The smallest zero is x = -10 as it is the least value on a number line.