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प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Determine the nature of the roots of the following quadratic equation:
2x2 - 6x + 3 = 0
उत्तर
2x2 - 6x + 3 = 0
Comparing the given quadratic equation with ax2 + bx + c = 0, we get
a = 2, b = -6, c = 3
Discriminant = b2 - 4ac
= (-6)2 - 4 (2) (3)
= 36 - 24
= 12
As b2 - 4ac > 0,
Therefore, distinct real roots exist for this equation
x = `(-b+-b^2-4ac)/(2a)`
= `(-(-6)+-sqrt((-6)^2-4(2)(3)))/(2(2))`
= `(6+-sqrt12)/4`
= `(6+-2sqrt3)/4`
= `(3+-sqrt3)/2`
Therefore, the root are `x=(3+sqrt3)/2 and x = (3-sqrt3)/2`
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