Question

the quadratic polynomial whose sum of zeroes is 3 and product of zeroes -2is​

Answer 1

Question:-

the quadratic polynomial whose sum of zeroes is 3 and product of zeroes -2 is

${\blue{\underline{\underline{\bold{Answer:-}}}}}$

According to the question,

sum of zeroes ==> 3

product of zeroes ==> -2

Let, the quadratic polynomial be ax^2+bx+c

So,,

3 = -b/a & -2 = c/a

If we take a = 1 , then b = -3 and c = -2

hope it helps you..

Answer 2

Question

the quadratic polynomial whose sum of zeroes is 3 and product of zeroes -2 is

Solution

Given :-

• Sum of zeroes = 3
• Product of zeroes = -2

Find :-

• Polynomial Equation

Explanation

Formula Of Equation

★ x² - (Sum of zeroes)x + (product of zeroes ) = 0

So, Now Keep Value of (Sum of zeroes ) & (product of zeroes )

➤▸ x² - x(3) + (-2) = 0

➤▸ x² - 3x - 2 = 0

Hence

Required Solution be

• x² - 3x - 2 = 0

__________________

Answer Verification

Factor of given equation , By Dharacharya Formula

★ x = [ {-b ± √(b²-4ac)}/2a]

Where,

• a = 1
• b = -3
• c = -2

Keep All Values

==> x = [{-(-3) ± √(-3)³ - 4 * 1 * (-2)}/2*1]

==> x = [ 3 ± √ (9+8)}/2]

==>x = (3 ± √17)/2

First Take -ve sign

==> x = (3 - √17)/2

Now, Take -ve sign

==> x = (3 + √17)/2

_______________________

So, Now we Calculate

==> Sum of zeroes = ( 3 + √17)/2 + (3 - √17)/2

==> Sum of zeroes = 6/2

==> Sum of zeroes = 3

And,

==> Product of zeroes = 3 + √17)/2 * (3 - √17)/2

==> Product of zeroes = ( 3² - √17²)/4

==> Product of zeroes = (9 - 17)/4

==> Product of zeroes = -8/4

==> Product of zeroes = -2

Proved

____________________