The square root of a real number can be positive or negative, and whether the roots of a quadratic equation are real or not can be determined by the discriminant. The discriminant is greater than zero, the equation has two distinct real roots.
NCERT Solutions for Class 10th Maths
Page No:91 Chapter 4 EXERCISE 4.3 Questions No:3 Part (iii).
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: 2x² – 6x + 3 = 0
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2x² – 6x + 3 = 0
The given equations is of the form ax² + bx + c = 0 in which a = 2, b = – 6, c = 3.
Therefore, D = b² – 4ac = (-6)² – 4 × 2 × 3 = 36 – 24 12 > 0
So, the roots of quadratic equation are real and unequal.
Hence, x = 6±√12/4 = 6±3√3/4 = 3±√3/2 [As x = -b±√b² – 4ac/2a]
Either x = 3±√3/2 or x = 3-√3/2
Hence, the roots of the quadratic equation are 3+√3/2 and 3-√3/2.