4x^2+19-5=0 using quadratic formula

STEP - STEP EXPLANATION:

Trying to factor by splitting the middle term

Factoring 4x2-19x-5

The first term is, 4x2 its coefficient is 4 .

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

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

Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20

Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -19 .

-20 + 1 = -19 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 1

4x2 - 20x + 1x - 5

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

4x • (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 :

(4x+1) • (x-5)

Which is the desired factorization

Equation at the end of step

2

:

(x - 5) • (4x + 1) = 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.

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f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

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-6 is the correct option from the above given options