Question

solve 3 x square - x - 4 = 0 in quadratic formulae ​

Answer 1

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution :

STEP

1

:

Equation at the end of step 1

(3x2 - x) - 4 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 3x2-x-4

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

The middle term is, -x its coefficient is -1 .

The last term, "the constant", is -4

Step-1 : Multiply the coefficient of the first term by the constant 3 • -4 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .

-12 + 1 = -11

-6 + 2 = -4

-4 + 3 = -1 That's it

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

3x2 - 4x + 3x - 4

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

x • (3x-4)

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

1 • (3x-4)

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

(x+1) • (3x-4)

Which is the desired factorization

Equation at the end of step

2

:

(3x - 4) • (x + 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.

Solving a Single Variable Equation:

3.2 Solve : 3x-4 = 0

Add 4 to both sides of the equation :

3x = 4

Divide both sides of the equation by 3:

x = 4/3 = 1.333

Solving a Single Variable Equation:

3.3 Solve : x+1 = 0

Subtract 1 from both sides of the equation :

x = -1

Supplement : Solving Quadratic Equation Directly

Solving 3x2-x-4 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Answer 2

Answer:

${3x}^{2} - x - 4 = 0 \\ {3x}^{2} + 3x - 4x - 4 = 0 \\ 3x(x + 1) - 4(x + 1) = 0 \\ (3x - 4)(x + 1) = 0 \\ \\ x + 1 = 0 \\ x = - 1 \\ \\ \\ \\ 3x - 4 = 0 \\ 3x = 4 \\ x = \frac{4}{3} \\ \\ \\ x = - 1, \frac{4}{3}$

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