Question

If α β are the zeroes of the polynomial f(x)=x²+x+1 , then 1 upon α + 1 upon β

Answer 1

AnsWer :

- 1.

SolutioN :

We have, Polynomial.

• Zero α and β.

$\tt \dagger \: \: \: \: \: {x}^{2} + x + 1.$

✎ Compare With General Expression of Polynomial.

$\tt \dagger \: \: \: \: \: a{x}^{2} + bx + c.$

Where as,

• a = 1.
• b = 1.
• c = 1.

☛ Now, Let's Find the value of

$\tt \dagger \: \: \: \: \: \dfrac{1}{ \alpha } + \dfrac{1}{ \beta } = \: \: ?$

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

$\tt : \implies \dfrac{ \alpha + \beta }{ \alpha \beta }$

$\tt : \implies \dfrac{ \dfrac{ - b}{ \cancel{a}} }{ \dfrac{c}{ \cancel{a}} }$

$\tt : \implies \dfrac{ - b }{ c }$

$\tt : \implies \dfrac{ - 1}{1}$

$\tt : \implies - 1.$

✡ Therefore, the value of 1 / α + 1 / β is - 1.