Question

if alpha and beta are zeroes of x2-3x+2 find alpha by beta +beta by alpha

​

Answer 1

Answer:

what is alfa bita gama............................

Answer 2

$\LARGE\underline{\underline{\orange{\bf{\mathfrak{\:Question}}}}}$

if $\sf{\:\alpha\:and\:\beta}$are zeroes of x²-3x+2 . find $\sf{\:\dfrac{\alpha}{\beta}\:+\:\dfrac{\beta}{\alpha}}$

$\LARGE\underline{\underline{\orange{\bf{\mathfrak{\:Answer}}}}}$

Given :-

• Equation x² - 3x + 2 = 0

Find:-

• . find $\sf{\:\dfrac{\alpha}{\beta}\:+\:\dfrac{\beta}{\alpha}}$.

$\LARGE\underline{\underline{\orange{\bf{\mathfrak{\:Explanation}}}}}$

We have ,

$\red{\boxed{\boxed{\green{\sf{\:sum\:of\:zeros\:=\:\dfrac{-(Coefficient\:of\:x)}{coefficient\:of\:x^2}}}}}}$

$\mapsto\sf{\:\alpha+\beta\:=\:\dfrac{-(-3)}{1}}$

$\mapsto\sf{\:\alpha+\beta\:=\:3}$.....[Equ(1)]

Again,

$\red{\boxed{\boxed{\green{\sf{\:Product\:of\:zeros\:=\:\dfrac{(Constant\:part)}{coefficient\:of\:x^2}}}}}}$

$\mapsto\sf{\:\alpha\beta\:=\:\dfrac{2}{1}}$

$\mapsto\sf{\:\alpha\beta\:=\:2}$.....[equ(2)]

__________________________

We Know,

$\:\:\:\:\:\:\small\pink{\sf{\:(a+b)^2\:=\:a^2+b^2+2ab}}$

$\mapsto\sf{\:(\alpha+\beta)^2\:=\:\alpha^2+\beta^2+2\alpha\beta}$

$\:\:\:\:\:\:\small\pink{\sf{\:Keep\:value\:by\:equ(1)}}$

$\mapsto\sf{\:(3)^2\:=\:\alpha^2+\beta^2+2\times2}$

$\mapsto\sf{\:(\alpha^2+\beta^2)\:=\:9-4}$

$\mapsto\sf{\:(\alpha^2+\beta^2)\:=\:5}$......[equ(3)]

Find:-

$\orange{\sf{\:\dfrac{\alpha}{\beta}\:+\:\dfrac{\beta}{\alpha}}}$

$\mapsto\sf{\:\dfrac{\alpha^2+\beta^2}{\alpha\beta}}$

$\:\:\:\:\:\:\small\pink{\sf{\:Keep\:value\:by\:equ(2)\:and\:equ(3)}}$

$\mapsto\sf{\:\dfrac{5}{2}}$

$\mapsto\pink{\sf{\:2.5}}$. [Ans]