Question

if x is equal to 1 is a common root of ax square+ax+2 is equal to 0 and xsquare+x+b is equal to 0 then a is to b is

Answer 1

$\text{1 is a root of} \: \: ax^2+ax+2=0\\ \\ \Rightarrow a \times {1}^{2} + a \times 1 + 2 = 0 \\ \\ \Rightarrow a + a + 2 = 0 \\ \\ \Rightarrow 2a = - 2 \\ \\ \Rightarrow a = - 1$


$\text{1 is a root of} \: \: x^2+x+b=0\\ \\ \Rightarrow {1}^{2} + 1 + b= 0 \\ \\ \Rightarrow 2 + b= 0 \\ \\ \Rightarrow b = - 2$


$a : b = ( - 1) : ( - 2) = 1 : 2 \\ \\ \boxed{ \red{a : b = 1 : 2}}$

Answer 2

Step-by-step explanation:

$\begin{lgathered}\text{1 is a root of} \: \: ax^2+ax+2=0\\ \\ \Rightarrow a \times {1}^{2} + a \times 1 + 2 = 0 \\ \\ \Rightarrow a + a + 2 = 0 \\ \\ \Rightarrow 2a = - 2 \\ \\ \Rightarrow a = - 1\end{lgathered}$

$\begin{lgathered}\text{1 is a root of} \: \: x^2+x+b=0\\ \\ \Rightarrow {1}^{2} + 1 + b= 0 \\ \\ \Rightarrow 2 + b= 0 \\ \\ \Rightarrow b = - 2\end{lgathered}$

$\begin{lgathered}a : b = ( - 1) : ( - 2) = 1 : 2 \\ \\ \Huge\boxed{ \green{a : b = 1 : 2}}\end{lgathered}$