Question

6x^2-13x+6 solve the factories questions​

Answer 1

Answer:

3/2 and 2/3 are the two zeroes

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Answer 2

The factors of $\bf 6 {x}^{2} - 13x + 6$ are $\bf \left(x - \frac{3}{2} \right)\left(x - \frac{2}{3}\right )$ and solution of quadratic equation are $\bf x = \frac{3}{2}$ and $\bf x = \frac{2}{3}$

Given:

$6 {x}^{2} - 13x + 6$

To find:

Factors and solution of quadratic polynomial.

Solution:

It can be solve by converting quadratic polynomial into quadratic equation.

Quadratic polynomial:

$a {x}^{2} + bx + c$ where a≠0

Quadratic equation:

$a {x}^{2} + bx + c = 0$

On inspection, it is clear that it can't be solve by factorisation. Thus apply quadratic formula.

Quadratic formula:

$\bf x_{1,2} = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a}$

Step 1:

Write coefficients of x²,x and constant term.

a=6

b=-13

c=6

Step 2:

Put the values in quadratic formula

$x_{1,2} = \frac{ 13 \pm \: \sqrt{ {( - 13)}^{2} - 4 \times 6 \times 6 } }{2 \times 6}$

or

$x_{1,2} = \frac{ 13 \pm \: \sqrt{ 169 - 144 } }{12}$

or

$x_{1,2} = \frac{ 13 \pm \: \sqrt{ 25 } }{12}$

or

$x_{1,2} = \frac{ 13 \pm \: 5}{12}$

or

taking (+) sign

$x_1 = \frac{13 + 5}{12}$

or

$x_1 = \frac{ 18}{12}$

or

$x_1 = \frac{3}{2}$

or taking (-) sign

$x_2 = \frac{13 - 5}{12}$

or

$x_2 = \frac{8}{12}$

or

$x_2 = \frac{2}{3}$

Two zeros of quadratic equation are

$x = \frac{3}{2} \: and \: x = \frac{2}{3} \:$

Step 3:

Find the factors.

If a and b are the zeros of quadratic equation than factors can be written as (x-a) and (x-b).

If factors are required, than we can write

$\left(x - \frac{3}{2} \right)\left(x - \frac{2}{3}\right )$

Thus,

Factors of quadratic polynomial are $\left(x - \frac{3}{2} \right)\left(x - \frac{2}{3}\right )$ and it's zeros are $x = \frac{3}{2} \: and \: x = \frac{2}{3}$

Learn more:

If p{x) = 2x2 + 4x + 6 is a quadratic polynomial then what is the value of sum of zeroes?

a) 0

b) 1

c) - 2

d) 4

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Learn completing square method :

Solve the quadratic equation 3x2 + 7x + 1 = 0 by

the method of completing the square

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