Question

If alpha and beta are roots of the equation x2+x+1=0 then alpha square+beta square ​

Answer 1

please refer to the above pic

Answer 2

If α , β are roots of the equation x² + x + 1 = 0 then α² + β² = - 1

Given :

α , β are roots of the equation x² + x + 1 = 0

To find :

The value of α² + β²

Solution :

Step 1 of 2 :

Find the sum of the roots and product of roots

Here the given Quadratic equation is

x² + x + 1 = 0

Now the roots are α , β

Sum of the roots

= α + β

= - b/a

= - 1

Product of the roots

= αβ

= c/a

= 1

Step 2 of 2 :

Find the value of α² + β²

α² + β²

= (α + β)² - 2αβ

= ( - 1)² - 2 × 1

= 1 - 2

= - 1

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