Question

solve the following equation by factorisation method 3x^2-x-10=0​

Answer 1

Answer: $x = \frac{-5}{3}$  OR  $x = 2$

Step-by-step explanation:

First you have to multiply the last term with the first term

$3x^{2}$ x -10 = $-30x^{2}$

Now you have to write down all the factors of 30

They are,

1 x 30

2 x 15

3 x 10

5 x 6

Now you have to see the sign of the number you got by multiplying (-30)

If the sign is +, then both factors will have same sign and should be added to obtain the coefficient of the middle term.

If the sign is -, then both factors will have different sign and should be subtracted to obtain the coefficient of the middle term.

As here, it is - then both would have different sign and should be subtracted to obtain the coefficient of the middle term.

In this case, coefficient of the middle term is -1, only 6 and 5 can be applicable. (6-5=1)

The largest number will receive the sign of the middle term. So -6 and +5

$3x^{2} - 6x +5x - 10 = 0$

$3x(x-2)+5(x-2) = 0$

$(3x+5) (x-2)$ = 0

Any number multiplied by 0 is 0.

Hence, we can come to a decision that either of the above expressions can be 0. So we can write it as,

$3x + 5=0$     or     $x - 2 =0$

     $3x = -5$                 $x = 2$

      $x = \frac{-5}{3}$

Hope it was helpful