Answer: The correct option is (D) x = −2, x = 10.
Step-by-step explanation: We are given to solve the following quadratic equation :
\(x^2-8x-20=0~~~~~~~~~~~~~~~~~~~~~(i)\)
We will be using the method of factorization to solve the given quadratic equation.
From equation (i), we have
\(x^2-8x-20=0\\\\\Rightarrow x^2-10x+2x-20=0\\\\\Rightarrow x(x-10)+2(x-10)=0\\\\\Rightarrow (x+2)(x-10)=0\\\\\Rightarrow x+2=0,~~~x-10=0\\\\\Rightarrow x=-2,~10.\)
Thus, the required solution is
x = −2, x = 10.
Hence, option (D) is CORRECT.
