Question

.............................6x2 - 19x = 0​

Answer 1

Refer to aatachment

Solve by myself

$Answer$

Finding the roots of the quadratic equation.

Answer 2

Answer:

2 result(s) found

x=

3

2

=0.667

x=

2

5

=2.500

See steps

Step by Step Solution:

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Step by step solution :

STEP

1

:

Equation at the end of step 1

((2•3x2) - 19x) + 10 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 6x2-19x+10

The first term is, 6x2 its coefficient is 6 .

The middle term is, -19x its coefficient is -19 .

The last term, "the constant", is +10

Step-1 : Multiply the coefficient of the first term by the constant 6 • 10 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -19 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -4

6x2 - 15x - 4x - 10

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

3x • (2x-5)

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

2 • (2x-5)

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

(3x-2) • (2x-5)

Which is the desired factorization

Equation at the end of step

2

:

(2x - 5) • (3x - 2) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.