Question

if a,b are the zeroes of x²+x+1 then 1/a+1/b=​

Answer 1

p(x) = x² + x + 1

Given,

• 1st Zeroes = a
• 2nd Zeroes = b

$\text{To find : } \: \rm \frac{1}{a} + \frac{1}{b}$

Here,

$\text{Sum of zeroes(a + b) } \: = \tt \bigg(\frac{ - b}{a} \bigg) \: \: \: \: = \frac{ - 1}{1} \: \: \: = \: \sf - 1$

$\text{Product of zeroes(ab) = } \tt \frac{c}{a} \: \: = \: \frac{1}{1} \: \: \: = \sf1$

Now,

Solving the given expression,

$\tt \to\frac{1}{a} + \frac{1}{b} \\ \\ \tt \to \frac{b + a}{ab} \\ \\ \to \tt \frac{a + b}{ab} = \frac{ - 1}{1} = \: \: \: \sf\red{ - 1}$