Answer:
option (A) is correct.
x = -2
Step-by-step explanation:
Given : equation \(3x^2+14x+16=0\)
We have to solve for x,
Consider the given equation \(3x^2+14x+16=0\)
we will solve the given quadratic equation using middle term split method, we have,
14x can be writen as 6x + 8x , we have,
\(3x^2+14x+16=0 \Rightarrow 3x^2+6x+8x+16=0\)
Taking 3x common from frst two terms and 8 common from lasttwo term , we have,
\(\Rightarrow 3x(x+2)+8(x+2)=0\)
Taking (x + 2) common, we have,
\(\Rightarrow (x+2)(3x+8)=0\)
Thus, Apply zero product rule, \(a\cdot b=0 \Rightarrow a =0 \ or\ b= 0\)
\(\Rightarrow (x+2)=0\) or \(\Rightarrow (3x+8)=0\)
\(\Rightarrow x=-2\) or \(\Rightarrow x=\frac{-8}{3}\)
Thus, option (A) is correct.
