Question

If l,m and n are the zeroes of the polynomial f(x)=2x^3 + 5x^2+6x+10 then the value of 1/l+1/m+1/n is​

Answer 1

Answer :

the value of 1/l+1/m+1/n is "–0.6"

Step-by-step explanation :

⇒ Cubic Polynomial :

• It is a polynomial of degree 3.

• General form :

    ax³ + bx² + cx + d

• Relation between zeroes and coefficients :

     ☆ Sum of zeroes = -b/a

     ☆ Sum of the product of zeroes taken two at a time = c/a

     ☆ Product of zeroes = -d/a

_______________________________

Given polynomial,

f(x) = 2x³ + 5x² + 6x + 10

⇒ It is of the form ax³ + bx² + cx + d

(comparing) : a = 2 , b = 5 , c = 6 , d = 10

l , m and n are the zeroes of the given polynomial.

From the relation between the zeroes and coefficients :

 ⮞ Sum of zeroes = -b/a

     l + m + n = -5/2

⮞ Sum of the product of zeroes taken two at a time = c/a

    lm + mn + nl = 6/2 = 3

⮞ Product of zeroes = -d/a

     lmn = -10/2 = -5

we have to find the value of 1/l + 1/m + 1/n

     $\boxed{\sf \dfrac{1}{l} + \dfrac{1}{m} + \dfrac{1}{n} = \ ?}$

$\sf \dfrac{1}{l} + \dfrac{1}{m} + \dfrac{1}{n} = \dfrac{mn}{lmn} +\dfrac{nl}{lmn} +\dfrac{lm}{lmn} \\\\\\ \dfrac{1}{l} + \dfrac{1}{m} + \dfrac{1}{n} = \dfrac{mn+nl+lm}{lmn} \\\\\\ \dfrac{1}{l} + \dfrac{1}{m} + \dfrac{1}{n} =\dfrac{3}{-5} \\\\\\ \dfrac{1}{l} + \dfrac{1}{m} + \dfrac{1}{n} = \dfrac{-3}{5} \\\\\\ \dfrac{1}{l} + \dfrac{1}{m} + \dfrac{1}{n} =-0.6$

Therefore, the value of 1/l+1/m+1/n is "–0.6"

Answer 2

Answer :

the value of 1/l+1/m+1/n is "–0.6"

Step-by-step explanation :

⇒ Cubic Polynomial :

It is a polynomial of degree 3.

General form :

   ax³ + bx² + cx + d

Relation between zeroes and coefficients :

    ☆ Sum of zeroes = -b/a

    ☆ Sum of the product of zeroes taken two at a time = c/a

    ☆ Product of zeroes = -d/a

_______________________________

Given polynomial,

f(x) = 2x³ + 5x² + 6x + 10

⇒ It is of the form ax³ + bx² + cx + d

(comparing) : a = 2 , b = 5 , c = 6 , d = 10

l , m and n are the zeroes of the given polynomial.

From the relation between the zeroes and coefficients :

⮞ Sum of zeroes = -b/a

    l + m + n = -5/2

⮞ Sum of the product of zeroes taken two at a time = c/a

   lm + mn + nl = 6/2 = 3

⮞ Product of zeroes = -d/a

    lmn = -10/2 = -5

we have to find the value of 1/l + 1/m + 1/n

     

Therefore, the value of 1/l+1/m+1/n is "–0.6"