Find the roots of the equation 25x(x + 1) = – 4.

1.	Find the roots of the equation 25x(x + 1) = – 4.
Answer» Given equation is 25x(x + 1) = -4 25x(x + 1) = -4 ⇒ 25x²+ 25x + 4 = 0 ⇒ 25x²+ 20x + 5x + 4 = 0 ⇒ 5x (5x + 4) + 1(5x + 4) = 0 ⇒ (5x + 4)(5x + 1) = 0 Now, either 5x + 4 = 0 therefore x = \(\frac{– 4}{5}\) Or, 5x + 1 = 0 therefore x = \(\frac{– 1}{5}\) Thus, the roots of the given quadratic equation are x = \(\frac{– 4}{5}\) and x = \(\frac{– 1}{5}\) respectively.

Answer»

Given equation is 25x(x + 1) = -4

25x(x + 1) = -4

⇒ 25x²+ 25x + 4 = 0

⇒ 25x²+ 20x + 5x + 4 = 0

⇒ 5x (5x + 4) + 1(5x + 4) = 0

⇒ (5x + 4)(5x + 1) = 0

Now, either 5x + 4 = 0 therefore x = \(\frac{– 4}{5}\)

Or, 5x + 1 = 0 therefore x = \(\frac{– 1}{5}\)

Thus, the roots of the given quadratic equation are x = \(\frac{– 4}{5}\) and x = \(\frac{– 1}{5}\) respectively.

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