Two distinct polynomials f(x) and g(x) are de | vedclass

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Question

(c)

We have,

$f(x)=x^2+a x+2$ and $g(x)=x^2+2 x+a$

Let $\alpha$ be the common root of $f(x)=0$ and $g(x)=0$.

$\frac{\alpha^2}{a^2-4}=\frac

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(c)

We have,

$f(x)=x^2+a x+2$ and $g(x)=x^2+2 x+a$

Let $\alpha$ be the common root of $f(x)=0$ and $g(x)=0$.

$\frac{\alpha^2}{a^2-4}=\frac{\alpha}{2-a}$

$\Rightarrow \alpha=\begin{array}{c}a^2-4 \ 2-a\end{array}=\frac{(a+2)(a-2)}{-(a-2)}=-(a+2)$

and $\quad \frac{\alpha}{2-a}=\frac{1}{2-a} \Rightarrow \alpha=1$

$	herefore \quad-(a+2)=1$

$a+2=-1 \Rightarrow a=-3$

Now $\quad f(x)+g(x)=0$

$	herefore x^2-3 x+2+x^2+2 x-3=0$

$2 x^2-x-1=0$

Sum of roots $=\frac{1}{2} \quad\left[\because \alpha+\beta=\frac{-b}{a}ight]$

Two distinct polynomials $f(x)$ and $g(x)$ are defined as follows:

$f(x)=x^2+a x+2 ; g(x)=x^2+2 x+a$.If the equations $f(x)=0$ and $g(x)=0$ have a common root, then the sum of the roots of the equation $f(x)+g(x)=0$ is

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