Question

If a and b are the zeros of the quadratic polynomial x2+x+1 then find the values of 1/a+1/b and a2+b2

Answer 1

Hey!

Given Equation :- x² + x + 1
and it's zeros are a and b


To find :- 1/a + 1/b and a² + b²

Solution :-

From the given Equation we can find the sum and product of Equation.

• Sum of Zeros =
$= \frac{ - coefficient \: \: \: \: of \: \: \: x}{coeff. \: \: \: of \: \: {x}^{2} }$


$a + b = \frac{ - 1}{1}$


• Product of Zeros =
$= \frac{constant \: \: term}{coeff. \: \: of \: {x}^{2} }$


$ab = \frac{1}{1}$



♯

$\frac{1}{a} + \frac{1}{b}$


$= \frac{b + a}{ab}$


$= \frac{ - 1}{1}$

$= - 1$


♯

${a}^{2} + {b}^{2} \\ \\ = ( {a + b)}^{2} - 2ab$


$= ( { - 1)}^{2} - 2 \times 1$


$= 1 - 2 \\ = - 1$

Answer 2

Answer:

the answer is —1

Step-by-step explanation:

hey mate