Question

For each of the following, find a quadratic polynomial whose sum and product

respectively of the zeroes are as given. Also find the zeroes of these polynomials

by factorisation.


(i)-8/3 , 4/3

(ii)21/8 , 5/16

Answer 1

Sum of roots = -8/3 .
Product of roots = 4/3

Now,
We know that,
Quadratic equation =>
x² - ( sum of roots) x + product of roots = 0 .

x² - ( -8/3)x + 4/3 = 0 .

x² + 8/3x + 4/3 = 0

3x² + 8x + 4 = 0 .

By Factorisation :-

x² + 2/3x + 2x + 4/3 = 0

x ( x + 2/3 ) + 2 ( x + 2/3 ) = 0

( x + 2 ) ( x + 2/3 ) = 0

x = -2 or -2/3

By Formula :-
Now, x = -8±√8²-4(3)(4) / 2(3)
x = -8 ± √ 64 - 48 / 6 = -8 ± √16 / 6 = -8 ± 4 / 6
x = -8 + 4 / 6 or -8 -4 /6
x = -2/3 , -2 .

=======================================

Sum of roots = 21/8
Product of roots = 5/16

Now,
We know that,
Quadratic equation =>
x² - ( sum of roots) x + product of roots = 0 .

x² - ( 21/8)x + 5/16 = 0 .

16x² - 42x + 5 = 0 .

By Factorisation :

16x² - 42x + 5 = 0

16x² - 2x -40x + 5 = 0

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

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

x = 5/2 or 1/8

By Formula :-


x = -(-42)± √ (42²) - 4(16)(5) / 2 (16 )

x = 42 ± √ 1764 - 320 / 32

x = 42 ± √ 1444 / 32

x = 42 ± 38 / 32

x = 80/32 or 4/32

x = 20 / 8 or 1/8

x = 5/2 or 1/8

Hope helped!

Answer 2

Refer to attachments And Hope it helps ok