Question

If α, β are the zeros of the polynomial p(x) = x2+x+1, then value of x is?

Answer 1

ANSWER:

Given

• α , β are the zeroes of the polynomial
• Then , x = α & β

TO FIND:

The value of x , that means we need to find α & β

Given quadratic equation

p(x) = x² + x + 1

Solving using quadratic equation formula

Quadratic equation formula ↓

$\small {\it{x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}$

Here,

a = 1, b = 1, c = 1

$\to \small{ \rm{x = \frac{ - 1 \pm \sqrt{ {1}^{2} - 4(1)(1) } }{2(1)} }}$

$\small \to {\rm{x = \frac{ - 1 \pm \sqrt{1 - 4} }{ 2} }}$

$\small \to{ \rm{x = \frac{ - 1 + \sqrt{ - 3} }{2} (or) \frac{ - 1 - \sqrt{ - 3} }{2} }}$

Hence α = -1 + √-3/2 & β = -1-√-3/2

Hence, x = - 1 ±√-3/2