1.

Find the roots of the quadratic equation 6x2 – x – 2 = 0.

Answer»

We have

6x2 – x – 2 = 6x2 + 3x – 4x – 2

= 3x (2x + 1) – 2 (2x + 1)

= (3x – 2)(2x + 1)

The roots of 6x2 – x – 2 = 0 are the values of x for which (3x – 2)(2x + 1) = 0

Therefore, 3x – 2 = 0 or 2x + 1 = 0,

i.e., x =2/3 or x =-1/2

Therefore, the roots of 6x2 – x – 2 = 0 are 2/3  and -1/2.

We verify the roots, by checking that 2/3 and -1/2 satisfy 6x2 – x – 2 = 0.



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