Question

4z2-8z+3

factorise it​

Answer 1

Step-by-step explanation:

4z^2 - 8z + 3

4z^2 - 6z - 2z + 3

2z ( 2z - 3 ) - 1 ( 2z + 3 ) = 0

( 2z - 1 ) ( 2z - 3 ) = 0

Z = 1/2, 3/2

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Answer 2

Answer:

The factors of given quadratic term

${4z^{2}-8z+3}$ are

$\boxed{z \: = 3} \: \: or \: \: \boxed{z \: = \frac{1}{2}}$

Step-by-step-explanation:

The given term is

${4z^{2}-8z+3}$

$4 {z}^{2} - 8z + 3 = 0\\ \\ \longrightarrow \: 4 {z}^{2} - 6z - 2z + 3 = 0 \\ \\ \longrightarrow \: 2z(z - 3) - 1(z - 3) = 0 \\ \\ \longrightarrow \: (z - 3) \: (2z - 1) = 0 \\ \\ \longrightarrow \: z - 3 = 0 \: \: or \: \: 2z - 1 = 0 \\ \\ \longrightarrow \: z = 3 \: \: or \: \: 2z = 1 \\ \\ \longrightarrow \: \boxed{z \: = 3} \: \: or \: \: \boxed{z \: = \frac{1}{2}}$

Additional Information:

1. Quadratic Equation :

An equation having a degree ‘2’ is called quadratic equation.

The general form of quadratic equation is

${ax^{2}+bx+c=0}$

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Factorisation method:

To factorize the given quadratic term, split the middle term such that the sign after it ( + ) or ( - ) is equal to the product of first and last term.

In the given question, ${4z^{2}-8z+3}$ the middle term is - 8z.

The product of first and last terms is 12x².

Hence, it is splited as -6x - 2x.

Because, ( - 6 ) & ( - 2 ) becomes ( - 8 ) also, their product is 12.