You visited us 1 times! Enjoying our articles? Unlock Full Access!

Harmonic Mean

If a, b are...

Question

If $a, b$ are the roots of $x^{2} + x + 1 = 0$ then $a^{2} + b^{2}$ is equal to

- 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $- 1$
Sum of the roots $\Rightarrow a + b = - 1$ ...(1)
Product of the roots $\Rightarrow a b = 1$ ...(2)
We know that,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$
$\Rightarrow a^{2} + b^{2} = (a + b)^{2} - 2 a b$
Substituting $(1)$ and $(2)$ in the above equation, we get
$\Rightarrow a^{2} + b^{2} = (- 1)^{2} - 2 (1)$
$∴ a^{2} + b^{2} = - 1$

Suggest Corrections

Similar questions

a, b

x^{2} + x + 1 = 0

(a^{2} + b^{2})

a, b, c, d

x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5 = 0

1 + a^{2} + b^{2} + c^{2} + d^{2}

a

b

x^{2} - 4 x + 3 = 0

(1 + a + a^{2} + a^{3} . . .) (1 + b + b^{2} + b^{3} + . . . .)

x^{2} + 2 x + 4 = 0,

\frac{1}{a^{2}} + \frac{1}{b^{2}} =

$x^{2} + a^{2} x + b = 0 a n d x^{2} + x + 1 = 0$ have a common roots which of the following is true.

Join BYJU'S Learning Program