Math, asked by 111purupc, 1 month ago

Find the quadratic Polynomial whose sum of zeroes is 9
and Product is 18. Hence find the zeroes of the Polynomial​

Answers

Answered by MayankBhardwaj21
1

Answer:

your answer here friend

Step-by-step explanation:

Given: Sum for zeroes =  (α+β)=8

Product of the zeroes = αβ=12

Required quadratic polynomial is  

x  

2

−(α+β)x+αβ=x  

2

−(8)x+12

Now , find the zeroes of the above polynomial.

Let f(x)=x  

2

−(8)x+12

= x  

2

−6x−2x+12

=(x−6)(x−2)

Substitute f(x)=0

(x−6)=0 or (x−2)=0  

⇒x=6 or x=2

2 and 6 are the zeroes of the polynomial .

Answered by llsmilingsceretll
1

We know:

  • P(x)={x²-(a+b)x+a+b}

\dashrightarrowSum(a+b)=9

\dashrightarrow product(ab)=18

Now Putting the values,

\dashrightarrow{x²-(9)x+18}

\dashrightarrowx²-9x+18

\dashrightarrowx²+6x-3x+18

\dashrightarrowx(x+6) - 3(x+6)

\dashrightarrow(x+6)(x-3)

Hence,

=> x+6=0

=> x= -6

=>. x-3=0

=> x= 3

therefore,

  • -6 and 3 are the zerose's of the given polynomial.
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