Question

Without actually calculating the zeroes,form a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial 5x2+2x-3

Answer 1

Step-by-step explanation:

Given Without actually calculating the zeroes, form a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial 5x2+2x-3

• Sum of zeroes of a quadratic polynomial is – b / a and product is c/a
• So a + b = - 2/5 and ab = - 3/5
• According to question
• Sum of zeroes of the polynomial is 1/a + 1/b
•                                                  = a + b / ab
•                                                   = - 2/5 / - 3/5
•                                                 = 2/3
• Product of zeroes of the polynomial is 1/ab
•                                                          = 1/- 3/5
•                                                          = - 5/3
• We know that a quadratic equation is of the form ax^2 + bx + c
•                                                                            = x^2 – 2/3 x – 5/3
•          Taking 3 as lcm  we get 3x^2 – 2x – 5 or 1/3 as a factor

Reference link will be

https://brainly.in/question/15923225

Answer 2

Without actually calculating the zeroes,form a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial 5x2+2x-3 is 3x^2 - 2x - 5.

A quadratic equation is given by,

x^2 - (sum of zeros)x + (product of zeros) = 0

Given quadratic equation,

5x^2 + 2x - 3 = 0

sum of zeros = α + β = -b/a = -2/5

product of zeros = αβ = c/a = -3/5

Now, let us find out the reciprocals,

1/α + 1/β = (α+β)/αβ = (-2/5) / (-3/5) = 2/3

1/αβ = 1/(-3/5) = -5/3

Hence the required quadratic equation is given by,

x^2 - (2/3)x + (-5/3) = 0

3x^2 - 2x - 5 = 0