Question

Find the roots of 2/5 x² - x – 3/5 = 0 by the factorisation of the corresponding quadratic polynomial.

Answer 1

Given, the quadratic equation is \(\frac 25\)x² - x - \(\frac 35\) = 0.

We have to find the roots of the equation by factorisation method.

The equation can be written as

2x² - 5x - 3 = 0

On factoring,

2x² - 6x + x - 3 = 0

2x(x - 3) + 1(x - 3) = 0

(2x + 1)(x - 3) = 0

Now, 2x + 1 = 0

2x = -1

x = \(-\frac 12\)

Also, x - 3 = 0

x = 3

Therefore, the roots of the equation are \(-\frac 12\) and 3.

Answer 2

Given, 2/5 x² - x - 3/5 = 0

⇒ 2x² - 5x – 3 = 0

By splitting the middle term,

⇒ 2x² - 6x + x – 3 = 0

Taking common in the expression,

⇒ 2x (x - 3) + 1 (x - 3) = 0

⇒ (2x + 1) (x - 3) = 0

∴ 2x + 1 = 0 and ∴ x – 3 = 0

∴ x = -1/2 and ∴ x = 3