Question

write a cubic polynomial whose zeroes add upto 12 and are in the ratio 1:2:3​

Answer 1

Given :  a cubic polynomial whose zeroes add upto 12 and are in the ratio 1:2:3​

To find :  cubic polynomial

Solution:

Let say  zeroes are

a , 2a & 3a

Sum of zeroes  a + 2a + 3a = 6a

6a = 12

=> a = 2

Zeroes are  2 , 4  , 6

Cubic polynomial

= (x - 2)(x - 4)(x - 6)

= (x - 2)(x² - 10x + 24)

= x³ - 10x² + 24x  - 2x² + 20x - 48

= x³ - 12x² + 44x - 48

x³ - 12x² + 44x - 48   is the cubic polynomial

Learn More:

Find a quadratic polynomial whose zeroes are 1/2 , 4 - Brainly.in

https://brainly.in/question/16158030

Find the quadratic polynomial whose zeroes are log 1000, log0.01*0.1

https://brainly.in/question/18047168

Answer 2

Given data : The zeroes of a cubic polynomial ar in the ratio 1:2:3, and those zeroes upon adding gives 12 as a result.

To find : The cubic polynomial.

Step by step solution :

As the zeroes are in the ratio 1:2:3,

Let x, 2x, 3x be the zeroes of the cubic polynomial p(x).

As per the given data, sum of the zeroes = 12

So, x + 2x + 3x = 12

  ⇒ 6x = 12

  ⇒ x = 2

As we got that x=2, the zeroes of the cubic polynomial are :

2, 2(2), 2(3) = 2, 4, 6 respectively.

With 2, 4, 6 as zeroes, the cubic polynomial p(x) will be :

p(x) = (x - 2)(x - 4)(x - 6)

⇒ p(x) = (x² - 2x - 4x + 8)(x - 6)

⇒ p(x) = (x² - 6x + 8)(x - 6)

⇒ p(x) = x³ - 6x² -6x² + 36x + 8x - 48

⇒ p(x) = x³ - 12x² + 44x - 48

Therefore, p(x) = x³ - 12x² + 44x - 48 is the cubic polynomial that satisfy the given conditions

Learn more :

1) In a cubic polynomial sum of zeros is 9 and product of zeros is 15 if zeros are in AP then find that cubic polynomial​.

https://brainly.in/question/15429245

2) Examples of trinomial,cubic polynomial,binomial and quadraic polynomial.

https://brainly.in/question/1272798