Question

Find the zeroes of the quardatic polynomial the sumof whose zeroes is 8 and their product is 12,hene find the zeroes of the polynomial

Answer 1

Solution :

It is given that,

• Sum of zeroes of the polynomial = 8
• Product of the zeroes = 12

We know that,

Quadratic polynomial = k [ x² - ( sum of zeroes ) x + ( product of zeroes ) ]

Substitute the given values. We get,

= k [ x² - ( 8 )x + 12 ]

= k [ x² - 8x + 12 ]

Here, k = 1

Hence, the quadratic equation is : x² - 8x + 12.

Now, in order to find the zeroes the given polynomial, we've to factorise it.

x² - 8x + 12

= x² - 2x - 6x + 12

= x ( x - 2 ) - 6 ( x - 2 )

= ( x - 6 ) ( x - 2 )

Now,

• x - 6 = 0 ; x = 6
• x - 2 = 0 ; x = 2

Therefore, 6 and 2 are the zeroes of the given polynomial.

$\rule{200}2$

Answer 2

Answer:

6 and 2 are the zeroes of the given polynomial.

Step-by-step explanation:

Solution :

It is given that,

Sum of zeroes of the polynomial = 8

Product of the zeroes = 12

We know that,

Quadratic polynomial = k [ x² - ( sum of zeroes ) x + ( product of zeroes ) ]

Substitute the given values. We get,

= k [ x² - ( 8 )x + 12 ]

= k [ x² - 8x + 12 ]

Here, k = 1

Hence, the quadratic equation is : x² - 8x + 12.

Now, in order to find the zeroes the given polynomial, we've to factorise it.

x² - 8x + 12

= x² - 2x - 6x + 12

= x ( x - 2 ) - 6 ( x - 2 )

= ( x - 6 ) ( x - 2 )

Now,

x - 6 = 0 ; x = 6

x - 2 = 0 ; x = 2

Therefore, 6 and 2 are the zeroes of the given polynomial.