If 2sin2⁡π8 is a root of the equation x2 + ax +b= 0, where a and b are rational numbers, then a – b is equal to

# If $2{\mathrm{sin}}^{2}\frac{\mathrm{\pi }}{8}$ is a root of the equation x2 + ax +b= 0, where a and b are rational numbers, then a - b is equal to

1. A

$-\frac{5}{2}$

2. B

$-\frac{3}{2}$

3. C

$-\frac{1}{2}$

4. D

$\frac{1}{2}$

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### Solution:

So, other root is $\frac{\sqrt{2}+1}{\sqrt{2}}$
sum of roots $=-\mathrm{a}=1-\frac{1}{\sqrt{2}}+1+\frac{1}{\sqrt{2}}=2⇒\mathrm{a}=-2$
Productof roots  $=1-\frac{1}{2}=\frac{1}{2}=\mathrm{b}$
$\mathrm{a}-\mathrm{b}=-2-\frac{1}{2}=-\frac{5}{2}$

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