Question

Q.6) The roots of the quadratic
equation 6x' - x - 2 = 0 are:

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Answer 1

Answer:

here's your answer mate

Answer 2

Step-by-step explanation:

There is a typing error in your question.

The quadratic equation should be :

6x^2 - x - 2.

Now we have to find the roots of this equation. What that means?

Logically it means the values of x for which the value of equation becomes 0. Lets find out first then it will be clear.

6x^2 - x -2 = 0. {equating to 0 as we want root}

You need to find two numbers whose product is (-12) and sum is (-1). This procedure of finding two such numbers can be tricky especially if you are not in practice. Luckily in our case it is easy.

3 × (-4) = (-12)

3 + (-4) = (-1).

So our two numbers are 3 and (-4). Using these two numbers we have to split the middle term of the equation and factorise that. Thats all, lets see:

6x^2 - x -2 = 0

=> 6x^2 - 4x + 3x - 2 = 0. { the value of (-x) still same}

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

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

=> x = (-1/2) or x = (2/3)

So your roots of equation are (-1/2) and (2/3).

note: if you plot the graph of above equation the curve will cut the x axis at the points (-1/2) and (2/3) exactly!!

If you find splitting the middle term, finding two such numbers or factorising difficult in few questions then there is a formula called Quadratic formula which directly gives you value of roots. No factorisation, only calculation.

It is like this:

x = {-(b) +- √(b^2-4ac) } / 2a

where a, b , c are coefficient of quadratic equations respectively.

If you are curious then go find it out.

Quadratics are fun to learn.