Question

for what value of `k`,the roots of equation 3x^2-10x+k=0are reciprocal of each other​

Answer 1

Answer:

The required value of k is 3

Step-by-step explanation:

Given :

The roots of equation 3x² - 10x + k = 0 are reciprocal of each other​

To find :

the value of k

Solution :

Let one zero be 'a'

As the other zero is reciprocal to the other, the other zero = 1/a

For the given quadratic polynomial,

x² coefficient = 3

x coefficient = -10

constant = k

we know,

Product of roots = constant/x² coefficient

So,

a × 1/a = k/3

 1 = k/3

 k = 3

∴ The value of k is 3.

__________________________

About Quadratic Polynomials :  

✯ It is a polynomial of degree 2  

✯ General form :  

  ax² + bx + c  = 0  

✯ Determinant, D = b² - 4ac  

✯ Based on the value of Determinant, we can define the nature of roots.  

D > 0 ; real and unequal roots  

D = 0 ; real and equal roots  

D < 0 ; no real roots  

✯ Relationship between zeroes and coefficients :  

 ✩ Sum of zeroes = -b/a  

 ✩ Product of zeroes = c/a  

_______________________________

Answer 2

Answer:

Given :

The roots of equation 3x² - 10x + k = 0 are reciprocal of each other​

To find :

the value of k

Solution :

Let one zero be 'a'

As the other zero is reciprocal to the other, the other zero = 1/a

For the given quadratic polynomial,

x² coefficient = 3

x coefficient = -10

constant = k

we know,

Product of roots = constant/x² coefficient

So,

a × 1/a = k/3

1 = k/3

k = 3

∴ The value of k is 3.

__________________________

About Quadratic Polynomials :  

✯ It is a polynomial of degree 2  

✯ General form :  

 ax² + bx + c  = 0  

✯ Determinant, D = b² - 4ac  

✯ Based on the value of Determinant, we can define the nature of roots.  

D > 0 ; real and unequal roots  

D = 0 ; real and equal roots  

D < 0 ; no real roots  

✯ Relationship between zeroes and coefficients :  

✩ Sum of zeroes = -b/a  

✩ Product of zeroes = c/a  

Step-by-step explanation:

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