Find the values of 𝑎 and b, if they are zeroes of the polynomial 𝑥² + 𝑎𝑥 + 𝑏.

For the polynomial $a{x}^2+bx+c$, the sum of its zeroes is $\frac{- b}{a}$ and product of its zeroes is $\frac{c}{a}$

The given polynomial is 𝑥² + 𝑎𝑥 + 𝑏 the zeroes of the given polynomial are a and b.

The sum of the zeroes of the polynomial 𝑎 + 𝑏 = −𝑎 

$\begin{array}{r}\Rightarrow a+b=-a\\ \Rightarrow b=-a-a\\ \Rightarrow b=-2a\cdots \end{array}$

The product of the zeroes of the given polynomial is 𝑎 × 𝑏 = 𝑏 

$\begin{array}{r}\Rightarrow a=\frac{b}{b}\\ \Rightarrow a=1\end{array}$

Putting the value in the equation (ⅰ) 

𝑏 = − 2(1) 

𝑏 = − 2 

Therefore, the value of 𝑏 is − 2. 

Hence, the value of 𝑎 and 𝑏 is 1 and 2, respectively.