the root for which the graph of [tex]f(x) = (x+4)^{6}(x+7)^{5}[/tex] cross the x-axis i.e. value of y or f(x) = 0 is [tex]x = -7[/tex] .
Step-by-step explanation:
We have , f(x) = (x + 4) 6(x + 7)5 i.e.[tex]f(x) = (x+4)^{6}(x+7)^{5}[/tex]. We need to find root for which the graph of [tex]f(x) = (x+4)^{6}(x+7)^{5}[/tex] cross the x-axis i.e. value of y or f(x) = 0. Let's solve this:
⇒ [tex]f(x) = (x+4)^{6}(x+7)^{5}[/tex]
⇒ [tex]0 = (x+4)^{6}(x+7)^{5}[/tex]
⇒ [tex](x+4)^{6}(x+7)^{5} = 0[/tex]
Which means either [tex]x+4 = 0\\x = -4[/tex] or , [tex]x+7=0\\x=-7[/tex] . That means the root for which the graph of [tex]f(x) = (x+4)^{6}(x+7)^{5}[/tex] cross the x-axis i.e. value of y or f(x) = 0 is [tex]x= -4[/tex] or [tex]x = -7[/tex] . ∴ From given options , the root for which the graph of [tex]f(x) = (x+4)^{6}(x+7)^{5}[/tex] cross the x-axis i.e. value of y or f(x) = 0 is [tex]x = -7[/tex] .
