If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x)=x^{2}-a x-b$, then the value of $(\al

Question

If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x)=x^{2}-a x-b$, then the value of $(\alpha+\beta+\alpha \beta)$ is equal to:\

Professor PC Thomas Classes · Answer

(c) Given polynomial is \ px= x$^2$ - ax  - b, and  $\alpha$ and  $\beta$ are zeroes  of p(x)
 Sum of zeroes  = $\alpha$ +  $\beta$m = a \ Product of  zeroes  = = $\alpha$ $\beta$m = -b \ Now, $\alpha$ + $\beta$+ $\alpha$ $\beta$ = a - b \ Concept Applied : If $\alpha$ and $\beta$ are the zeroes and quadratic polynomial p(x) = ax$^2$ + bx +c, then $\alpha$ + $\beta$ = - b/a, $\alpha$ $\beta$ = c/a