Question

If a.B are thr zeroes of the polynomial f(x) =x2+x+1then1÷a+1÷b​

Answer 1

Question :

If a and b are the Zeroes of the polynomial f(x) =x²+x+1. then, 1/a +1/b ?

AnsWer :

-1.

Required Concepts :

$\: \: \: \star \: \tt\alpha + \beta = \frac{ - b}{a} \\ \: \: \: \star \: \tt \alpha \times \beta = \frac{c}{a} \\ \tt \: \: \: \star \: \frac{1}{a} + \frac{1}{b} = \frac{a + b}{ab}$

Solution :

We have,

$\tt \: f(x) = {x}^{2} + x + 1.$

then,

$\tt \: \frac{1}{a} + \frac{1}{b} = \frac{a + b}{ab} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt = \frac{ - 1}{1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt = - 1.$

Therefore,the value of 1/a + 1/b is -1.

Some information :

-Polynomial have real zeros and algebraic expression.

-Highest degree of polynamial is 2.

have expression,

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

Where,

$\tt \: a \cancel = 0.$