Which of the following is equivalent to 7x^2- 27x - 4? A) (x + 4)(7x - 1)B) (x - 2)(7x + 2)C) (x + 2)(7x - 2)E) x(7x - 27 - 4)

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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

 7x^2- 27x - 4

This equation is a quadratic equation of type Ax^2 + Bx + C 

Now, here A = 7 ; B = -27 & C = -4

A*C = -28

B^2 = 729

Now, -27 = -28 + 1

Thus, the equation can be rewritten as 7x^2 - 28x + x - 4 

or, 7x(x-4) +1(x-4)

or, (7x+1)*(x-4)

So, none of the given options are correct.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to determine which of the given options is equivalent to 7x^2- 27x - 4.

7x^2 - 27x - 4 = 0

=> 7x^2 - 28x + x - 4 = 0

=> 7x(x - 4) + 1(x - 4) = 0

=> (7x + 1)(x - 4)

The options are:

A) (x + 4)(7x - 1) = 7x^2 + 28x - x - 4 = 7x^2 + 27x - 4

B) (x - 2)(7x + 2) = 7x^2 - 14x + 2x - 4 = 7x^2 - 12x - 4

C) (x + 2)(7x - 2) = 7x^2 + 14x - 2x - 4 = 7x^2 + 12x - 4

E) x(7x - 27 - 4) = 7x^2 - 27x - 4x = 7x^2 - 31x

None of the options given are equivalent to the given expression. The factorized form of 7x^2- 27x - 4 = (7x + 1)(x - 4)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

All we have to do is to determine the roots of the quadratic, knowing the fact that the quadratic is the result of the product of two linear factors: (x-x1)(x-x2), where x1 and x2 are the roots of the quadratic.

We'll determine the roots applying quadratic formula:

x1 = [27+sqrt(729+112)]/14

x1=(27+sqrt841)/14

x1=(27+29)/14

x1=4

x2 = -1/7

We'll write the quadratic:

(x-x1)(x-x2)=(x-4)(x+1/7) = (x-4)(7x+1)

The correct answer is: (x - 4)(7x + 1).

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