If - is a root of 4 x2-2 x-1-0- then root is-A- 4 -3-3 -B- 3 -3-4 -C- None of theseD- 4 -3-3 -

The correct option is D α is a root ⇒ 4α^2 + 2α 1 =0 4α^3 3α = ( α 1/2 ) (4α^2+2α 1) α 1/2 = α 1/2 if β is other root, then α+β = 1/2 ⇒β = α 1/2 hence 4 ...

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Byju's Answer

Standard XI

Mathematics

nth Root of a Complex Number

If α is a roo...

Question

If $α$ is a root of $4 x^{2} + 2 x - 1$ = 0. then root is:

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Solution

The correct option is C

$α$ is a root $\Rightarrow 4 α^{2} + 2 α - 1$ =0

$4 α^{3} - 3 α$ = $(α - \frac{1}{2})$ $(4 α^{2} + 2 α - 1)$ - $α$ - $\frac{1}{2}$ = $- α - \frac{1}{2}$

if $β$ is other root, then $α + β$ = $- \frac{1}{2}$ $\Rightarrow β$ = $- α - \frac{1}{2}$

hence $4 α^{3} - 3 α$ is other root.

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If α is a root of 4x2+2x−1 = 0. then root is:

The correct option is C α is a root ⇒4α2+2α−1 =0 4α3−3α = (α−12) (4α2+2α−1)-α-12 = −α−12 if β is other root, then α+β = −12 ⇒β = −α−12 hence 4α3−3α is other root.

If $α$ is a root of $4 x^{2} + 2 x - 1$ = 0. then root is: