Question

6.If alpha and beta are the zeroes of the polynomial 3x^(2)+5x+2 then the value of alpha+beta+alpha beta is​

Answer 1

$\star$ Question : If α and βare the zeroes of the polynomial 3x²+5x+2 then the value of α+βα.β is

$\star$ Answer :

$\alpha +\beta +\alpha .\beta =-1$

$\star$ Explanation :

$\star$ Given polynomial is 3x²+5x+2.

$\star$ Let α , β are zeroes of the polynomial.

$\star$ Let the general polynomial be ax²+bx+c.

$\star$ Compare this with given polynomial , we get ,

$\star$  a=3 , b=5 , c=2.

$\bold{\star}$ So , sum of roots of the polynomial is ,

$=>\alpha +\beta =\frac{-b}{a}=\frac{-5}{3}$

$\bold{\star}$ Product of roots of the polynomial is ,

$=>\alpha .\beta =\frac{c}{a}=\frac{2}{3}$

$\bold{\star}$ So , the value of $\alpha +\beta +\alpha .\beta$ is ,

$=>\alpha +\beta +\alpha .\beta \\\\=>\frac{-5}{3}+\frac{2}{3}\\\\ =>\frac{-3}{3}\\\\ =>-1$

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Answer 2

Answer:

 Question : If α and βare the zeroes of the polynomial 3x²+5x+2 then the value of α+βα.β is

\star⋆ Answer :

\alpha +\beta +\alpha .\beta =-1α+β+α.β=−1

\star⋆ Explanation :

\star⋆ Given polynomial is 3x²+5x+2.

\star⋆ Let α , β are zeroes of the polynomial.

\star⋆ Let the general polynomial be ax²+bx+c.

\star⋆ Compare this with given polynomial , we get ,

\star⋆  a=3 , b=5 , c=2.

\bold{\star}⋆ So , sum of roots of the polynomial is ,

= > \alpha +\beta =\frac{-b}{a}=\frac{-5}{3}=>α+β=a−b=3−5

\bold{\star}⋆ Product of roots of the polynomial is ,

= > \alpha .\beta =\frac{c}{a}=\frac{2}{3}=>α.β=ac=32

\bold{\star}⋆ So , the value of \alpha +\beta +\alpha .\betaα+β+α.β is ,

\begin{gathered}= > \alpha +\beta +\alpha .\beta \\\\= > \frac{-5}{3}+\frac{2}{3}\\\\ = > \frac{-3}{3}\\\\ = > -1\end{gathered}=>α+β+α.β=>3−5+32=>3−3=>−1