Question

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

Answer 1

Given

sum of the quadratic polynomial is 21/8

product of the quadratic polynomial is 5/16

To Find

We have to find the quadratic equation

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Since, we dont know the quadratic equation whose sum and product is given so,we apply sum and Product of zeroes formula:

Quadratic equation can be find by given formula:

x²-(sum of its zeroes)x + product of its zeroes

Sum of its zeroes = 21/8

product of its zeroes = 5/16

Now,put values into formula

$\sf = > {x}^{2} - \dfrac{21}{8} x + \dfrac{5}{16}$

Taking LCM of the term :

LCM is 16

$\sf = > \dfrac{16 {x}^{2} - 21(2)x + 5}{16}$

$\sf = > \dfrac{16 {x}^{2} - 42x + 5}{16} = 0$

$\sf = > 16 {x}^{2} - 42x + 5 = 0$

Hence,16x²-42x+5 is the required quadratic polynomial

Check:

16x²-42x+5

a=16 ,b= -42 & c= 5

Sum of its zeroes = -b/a = -(-42)/16= 42/16=21/8

product of its zeroes= c/a= 5/16