The quadratic formula is only used to find the roots of a quadratic equation.
The quadratic formula states that the solutions to this equation, also known as the roots of the equation.
To find the roots of the equation and solve the roots of the quadratic equations.
The values of the variable (usually x) that make the equation true.
NCERT Books Solutions for Class 10th Maths for 2022-2023.
Chapter 4 EXERCISE 4.3 Questions No:3 Part (ii)
Find the roots of the following equations: 1/x + 4 – 1/x – 7 = 11/30, x ≠ – 4, 7
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1/x + 4 – 1/x – 7 = 11/30, x ≠ – 4, 7
⇒ (x -7) – (x +4)/(x + 4)(x – 7) = 11/30
⇒ – 11/x² – 3x – 28 = 11/30
⇒ x² – 3x – 28 = – 30
⇒ x² – 3x + 2 = 0
For the quadratic equation x² – 3x + 2 = 0,we have a = 1, b = – 3, c = 1.
Therefore, b² – 4ac = (-3)² – 4 × 1 × 2 = 9 – 8 = 1 >
Hence, x = (3±√1)/2 = (3±1)/2 [As x = (-b±√b²-4ac)/2a
Either, x = 3+1/2 = 4/2 = 2 or x = 3-1/2 = 2/2 = 1
Hence, the roots of the quadratic equation are 2 and 1.