Question

find quadratic polynomial whose sum and product of zeros are given also find zeros of the polynomial by factorization 21/8,5/16​

Answer 1

||✪✪ CORRECT QUESTION ✪✪||

find quadratic polynomial whose sum and product of zeros are given as 21/8 ans 5/16. also find zeros of the polynomial by factorization ..

|| ★★ FORMULA USED ★★ ||

→ Equation with sum and product of roots is given by x² - (sum of roots)x + Product of roots = 0

|| ✰✰ ANSWER ✰✰ ||

we have given ,

→ sum of roots = (21/8)

→ Product of roots = (5/16)

So,

The required Quadratic Equation is :-

→ x² - (sum of roots)x + Product of roots. = 0

→ x² - (21/8)x + (5/16) = 0

Taking LCM now, we get,

→ (16x² - 42x + 5) /16 = 0

→ 16x² - 42x + 5 = 0

Splitting the middle term now, we get,

→ 16x² - 2x - 40x + 5 = 0

→ 2x(8x - 1) - 5(8x - 1) = 0

→ (2x - 5) (8x - 1) = 0

Putting both Equal to Zero now, we get,

→ 2x - 5 = 0

→ 2x = 5

→ x = (5/2) .

and,

→ 8x - 1 = 0

→ 8x = 1

→ x = (1/8) .

Hence, we can say that, The Required Quadratic Equation is 16x² - 42x + 5 = 0 and Its zeros are (5/2) and (1/8) ..

Answer 2

we know that :-

A Equation with sum and product of roots is given by x² - (sum of roots)x + Product of roots = 0

ANSWER :-

putting values we get,

x² - (21/8)x + (5/16) = 0

Taking LCM

=> (16x² - 42x + 5) /16 = 0

=> 16x² - 42x + 5 = 0

Splitting the middle term now

=> 16x² - 2x - 40x + 5 = 0

=> 2x(8x - 1) - 5(8x - 1) = 0

=> (2x - 5) (8x - 1) = 0

Now,

=> 2x - 5 = 0

=> 2x = 5

=> x = 5/2

or,

=> 8x - 1 = 0

=> 8x = 1

=> x = 1/8

So, Its zeros are (5/2) and (1/8).