Question

find the quadric polynomial, sum of whose zeroes is 8 and their product is 12,find other zeroes of polynomial ​

Answer 1

Answer:

Step-by-step explanation:

Let the quadratic polynomial be f (x) = ax2 + bx + c and its zeros be  and  

Then  +  = 8 =  and   = 12 =  

If a = 1, then b = -8 and c = 12            

Hence the quadratic polynomial is x2 - 8x + 12

Splitting the middle term, you get

x2 - 8x + 12 = (x - 6) (x - 2)

The zeros of f (x) are given by f (x) = 0

(x - 6) (x - 2) = 0

(x - 6) = 0 or (x - 2) = 0

x = 6 or x = 2

Hence the zeros of f (x) are:  = 6 and  = 2

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Answer 2

$\large\bf\underline \orange{Given:-}$

sum of zeroes = 8

product of zeroes = 12

$\large\bf\underline \orange{To \: find:-}$

quadratic polynomial.

$\huge\bf\underline \green{Solution:-}$

Let α and β are the zeroes of the required polynomial f(x).

Then,

• α + β = 8
• αβ = 12

• f(x) = x² - (α + β)x + αβ

➝ x² - (8)x + 12

➝ x² - 8x + 12

So, the required polynomial f(x) is x² -8x + 12

Verification :-

• Sum of zeroes = -b/a

➝ 8 = -(-8)/1

➝8 = 8

• Product of zeroes = c/a

➝ 12 = 12/1

➝ 12 = 12

LHS = RHS

Hence Verified .

Other zeroes are as :-

➝ x² -8x + 12

➝ x² - 2x - 6x + 12

➝ x(x - 2) -6(x -2)

➝ (x - 6)(x - 2)

➝ x = 6 or x = 2

So, the other zeroes are 6 and 2