Find the quadratic polynomial whose sum and product of the zeroes are 21/8 and
5/16 respectively.

We need to find the quadratic polynomial given that the sum and product of the zeroes are 21/8 and 5/16 respectively
It is known that the quadratic equation can be written as
𝑥² − (𝑆𝑢𝑚 𝑜𝑓 𝑟𝑜𝑜𝑡𝑠)𝑥 + (𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑟𝑜𝑜𝑡𝑠) = 0. For example, if α and β are the roots of a quadratic equation, then the quadratic equation is   2 .
Since it is given that the sum of roots is 21/8  and the product of roots is 5/16 , on substituting
the values, we get the quadratic equation as
𝑥² − (𝑆𝑢𝑚 𝑜𝑓 𝑟𝑜𝑜𝑡𝑠)𝑥 + (𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑟𝑜𝑜𝑡𝑠) = 0
⇒ 𝑥²− ( 21/8 )𝑥 +   5/16 = 0

⇒   1/16[16𝑥²  −  42𝑥  +  5] =  0
⇒ 16𝑥² − 42𝑥 + 5 = 0
Hence, the required quadratic equation is  16𝑥² − 42𝑥 + 5 = 0