Question

Find the solution set of the equation 3x2 - 8x - 3 = 0; when :
(i) XE Z (integers) (ii) x Q (rational numbers).​

Answer 1

Answer:

3x²-8x-3 = 0

3x²-9x+x-3 = 0

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

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

3x+1 = 0 or x-3 = 0

x = -1/3 or x = 3

i) x = {-1/3,3}

ii) x = {-1/3,3}

Answer 2

Answer:

The set of solution belongs to integers is {3}

The set of solution belongs to rational numbers is {3,-1/3}.

Step-by-step explanation:

We are given the equation $3x^2-8x-3=0$.

We are asked to find the solution set of equation $3x^2-8x-3=0$ when X belongs to integers and X belongs to Rational numbers.

Let us factorise the given equation.

$3x^2-8x-3=0$

$3x^2-9x+x-3=0$

Take 3x as common from the first two terms

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

Take 1 as common from third and fourth terms.

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

Take x-3 as common from both the terms.

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

$(x-3)=0$ and  $(3x+1)=0$

$x=3$   and   $3x+1=0$

                          $3x=-1$

                            $x=-1/3$

Therefore,

The set of solution belongs to integers is {3}

The set of solution belongs to rational numbers is {3,-1/3}.