The values of the variable (usually x) that make the equation true.
Quadratic formula to find the roots.
NCERT Solutions for Class 10th Maths.
Page No:88 Chapter 4 EXERCISE 4.3 Important Questions No:3 Part (i)
Find the roots of the following equations: x – 1/x = 3, x ≠ 0
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x – 1/x = 3, x ≠ 0
⇒ x² – 1 = 3x
⇒ x² – 3x – 1 = 0
For the quadratic equation x² – 3x – 1 = 0, we have a = 1, b = – 3 and c = – 1.
Therefore, b² – 4ac = (-3)² – 4 × 1 × (-1) = 9 + 4 = 13 > 0
Hence, x = (3 ± √13)/2 [As x = (-b ±√(b²- 4ac))/2a]
Either x = (3 + √13)/2 or x = (3 – √13)/2
Hence, the roots of the quadratic equation are (3 + √13)/2 and (3 – √13)/2.