What are the best way for solving ncert 10th solution, of quadratic equation exercise 4.4. How i solve this question in easy way Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;(iii) 2×2 – 6x + 3 = 0
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Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;(iii) 2×2 – 6x + 3 = 0 Q.1(3)
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2x2 – 6x + 3 = 0
Comparing the equation with ax2 + bx + c = 0, we get
a = 2, b = -6, c = 3
As we know, Discriminant = b2 – 4ac
= (-6)2 – 4 (2) (3)
= 36 – 24 = 12
As b2 – 4ac > 0,
Therefore, there are distinct real roots exist for this equation, 2x2 – 6x + 3 = 0.
= (-(-6) ± √(-62-4(2)(3)) )/ 2(2)
= (6±2√3 )/4
= (3±√3)/2
Therefore the roots for the given equation are (3+√3)/2 and (3-√3)/2