Question

Without actually calculating the zeroes, form a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial 5x^2 + 2x - 3.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

3x^2 - 2x - 5

Step-by-step explanation:

We know sum of zeroes in a quadratic polynomial is -b/a and product is c/a

So ,

Sum of zeroes polynomial 5x^2 + 2x - 3 is -2/5 and product is -3/5

α+β  = -2/5

αβ= -3/5

Given zeroes of polynomial to find would be the reciprocals of given polynomial

Sum of zoroes on 2nd polynomial is = 1/α + 1/β

                                                             =α+β/αβ

                                                             =(-2/5)/(-3/5)

                                                             =2/3

Product of zeroes of 2nd polynomial is = 1/αβ

                                                                 =-5/3

now to construct a polynomial we know every quadratic polynomial is in the form

k(x-α)(x-β)

kx^2 - k(sum of zeroes)x + k(product of zeroes)

=>x^2 - 2/3x - 5/3

now taking 1/3 common

=>1/3(3x^2-2x-5)

here as 1/3 can be taken as a factor so

the polynomial is => 3x^2-2x-5

now taking 1/3 common