Find the roots of the equation 48x2 – 13x – 1 = 0.

1.	Find the roots of the equation 48x2 – 13x – 1 = 0.
Answer» Given equation is 48x²– 13x – 1 = 0. ⇒ 48x²– 13x – 1 = 0. ⇒ 48x²– 16x + 3x – 1 = 0. ⇒ 16x(3x – 1) + 1(3x – 1) = 0 ⇒ (16x + 1)(3x – 1) = 0 Either 16x + 1 = 0 ⇒ x = \(\frac{-1}{16}\) Or, 3x – 1=0 ⇒ x = \(\frac{1}{3}\) Thus, the roots of the given quadratic equation are x = \(\frac{-1}{16}\) and x = \(\frac{1}{3}\) respectively.

Answer»

Given equation is 48x²– 13x – 1 = 0.

⇒ 48x²– 13x – 1 = 0.

⇒ 48x²– 16x + 3x – 1 = 0.

⇒ 16x(3x – 1) + 1(3x – 1) = 0

⇒ (16x + 1)(3x – 1) = 0

Either 16x + 1 = 0 ⇒ x = \(\frac{-1}{16}\)

Or, 3x – 1=0 ⇒ x = \(\frac{1}{3}\)

Thus, the roots of the given quadratic equation are x = \(\frac{-1}{16}\) and x = \(\frac{1}{3}\) respectively.

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