Question

5. A = { x:x is a factor of 18 } and B = { x:x is a composite number less than or

equal to 15} and n(A) and n(B) are the same and product of zeroes of a

polynomial then find the polynomial .​

Answer 1

Question:

Two sets A and B are such that,

A = {x : x is a factor of 18}

B = {x : x is a composite number less than or equal to 15}

The no. of elements in the sets, n(A) and n(B), are the sum and the product of zeroes of a quadratic equation respectively. Find the quadratic equation.

Solution:

First let's find the two sets A and B.

A = {1, 2, 3, 6, 9, 18}

B = {4, 6, 8, 9, 10, 12, 14, 15}

Then,

n(A) = 6 $\quad$

n(B) = 8

Since the sum of the zeroes of the quadratic equation is n(A) and the product is n(B), the quadratic equation is,

x² - n(A)x + n(B) = 0

That is,

x² - 6x + 8 = 0