Question

Find the roots of the following quadratic equations by factorisation:
3x2 — 14x — 5 = 0

Answer 1

Question:

Find the roots of the following quadratic equation by factorisation : 3x² - 14x - 5 = 0

Answer:

x = 5 , -1/3

Note:

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

Solution:

The given quadratic equation is :

3x² - 14x - 5 = 0 .

Now ,

Splitting the middle term of the given quadratic equation, we have ;

=> 3x² - 14x - 5 = 0

=> 3x² - 15x + x - 5 = 0

=> (3x² - 15x) + (x - 5) = 0

=> 3x(x - 5) + (x - 5) = 0

=> (x - 5)•(3x + 1) = 0

Case1 : x - 5 = 0

=> x - 5 = 0

=> x = 5

Case2 : 3x + 1 = 0

=> 3x + 1 = 0

=> 3x = -1

=> x = -1/3

Hence,

The required roots of the given quadratic equation are : x = 5 , -1/3 .

Answer 2

Answer:

$hey$

Step-by-step explanation:

Factoring  3x2-14x-5 

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -14x  its coefficient is  -14 .

The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -5 = -15 

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   -14 .

     -15   +   1   =   -14   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  1 

                     3x2 - 15x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                    3x • (x-5)

              Add up the last 2 terms, pulling out common factors :

                     1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                    (3x+1)  •  (x-5)

             Which is the desired factorization.

I HOPE IT WILL HELP YOU