Question

if alpha and beta are zeroes of poly 4x sqaure +4x-1 then 1/alpha +1/beta is​

Answer 1

Answer :

1/α + 1/ß is 4

Given :

The quadratic polynomial is

• 4x² + 4x - 1
• α and ß are the zeroes of the given polynomial

To Find :

The Value of

$\sf \bullet \: \: \dfrac{1}{\alpha}+\dfrac{1}{\beta}$

Concept to be used :

Relationship between the zeroes and the coefficients of the polynomial

$\sf \star \: \: Sum \: of \: the \: zeroes =-\dfrac{Coefficient \: of \: x}{Coefficient \: of \: x^{2}} \\\\ \sf \star \: \: Product\: of \: the \: zeroes=\dfrac{Constant \: term}{Coefficient \: of \: x^{2}}$

Solution :

Given polynomial is :

$\sf 4x^{2} + 4x - 1$

From the relations of sum we have

$\sf \implies \alpha + \beta =-\dfrac{4}{4}\\\\ \sf \implies \alpha + \beta = -1..........(1)$

Again from product relation

$\sf \implies \alpha \beta = \dfrac{-1}{4} \\\\ \sf \implies \alpha\beta = -\dfrac{1}{4}...........(2)$

Dividing (1) by (2) we have

$\sf \implies \dfrac{\alpha}{\alpha\beta}+\dfrac{\beta}{\alpha\beta} = \dfrac{ -1}{-\dfrac{1}{4}}\\\\ \sf \implies \dfrac{1}{\beta}+\dfrac{1}{\alpha}= 4 \\\\ \sf \implies \dfrac{1}{\alpha}+\dfrac{1}{\beta}= 4$

Therefore , required value is 4