Question

If alpha and beta are two zeros of plynomial x^2+x+1 than find 1\alpha+1/beta

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

A polynomial

X²+x-12

${\sf{\green{\underline{\large{To\:Find}}}}}$

• Factors of the polynomial

$\tt\dfrac{1}{\alpha}+\dfrac{1}{\beta}$

• Relationship between cofficient

${\sf{\pink{\underline{\Large{Explanation}}}}}$

X²+x-12

• we have to spilt the middle term in such a way that the product become -12 and sum become x

X²+X+12

=>X²+4x-3x-12

=>x(x+4)-3(x+4)

=>(x-3) (x+4)

=>x=3,-4

Let the zeroes of the polynomial be$\tt\alpha{and}\beta$

Then,

$\rightarrow\tt\alpha{+}\beta{=}\frac{-b}{a}$

&

$\rightarrow\tt\alpha{\times}\beta{=}\frac{c}{a}$

Here,

a=1

b=1

C=-12

☞

Here

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{-1}{1}$

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{-12}{1}$

Solving

$\tt\dfrac{1}{\alpha}+\dfrac{1}{\beta}$

$\rightarrow\tt\dfrac{1}{\alpha}+\dfrac{1}{\beta}$

$\rightarrow\tt\dfrac{\alpha+\beta}{\alpha\beta}$

Putting values

=>-1/-12

=>1/12

Additional Information

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{-1}{1}$

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{Cofficient\:of\:X}{Cofficient\:of\:x^2}=$

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{-12}{1}$

$\rightarrow\tt{\large\alpha{\times}\beta{=}\dfrac{Constant\:term}{Cofficient\:of\:x^2}}$

Hence,relation verified