The given expression is :
[tex]0=x^2+3x-10[/tex]Factorize the expression :
[tex]\begin{gathered} 0=x^2+3x-10 \\ x^2+3x-10=0 \end{gathered}[/tex]Find the pair of number such that : the product of two numbers are equal = (-10)
and thier summation is equal to 3
i.e. 5 x ( -2) = -10 and 5 + (-2) = 3
So,
[tex]\begin{gathered} x^2+3x-10=0 \\ x^2+5x-2x-10=0 \end{gathered}[/tex]Take x common from the first two terms and (-2) from last two terms :
[tex]\begin{gathered} x^2+5x-2x-10=0 \\ x(x+5)-2(x+5)=0 \\ \text{Now, take (x+5) common :} \\ (x-2)(x+5)\text{ =0} \end{gathered}[/tex]Now equate each factor with zero :
[tex]\begin{gathered} (x-2)(x+5)=0 \\ x-2=0\Rightarrow x=2 \\ x+5=0\Rightarrow x=-5 \end{gathered}[/tex]Answer : C) x = -5, 2
