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प्रश्न
Find the roots of the following equation, if they exist, by applying the quadratic formula:
`2x^2 - 2sqrt(2)x + 1 = 0`
बेरीज
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उत्तर
Given: `2x^2 - 2sqrt(2)x + 1 = 0`
Step-wise calculation:
1. Identify coefficients:
a = 2, b = `-2sqrt(2)`, c = 1
2. Discriminant:
D = b2 – 4ac
= `(-2sqrt(2))^2 - 4(2)(1)`
= 8 – 8
= 0
3. Since D = 0, the quadratic has real and equal roots.
4. Quadratic formula:
`x = (-b ± sqrt(D))/(2a)`
= `(-(-2sqrt(2)) ± 0)/(4)`
= `(2sqrt(2))/4`
= `sqrt(2)/2`
The equation has a repeated root `x = sqrt(2)/2` (multiplicity 2).
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