Question

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

Answer 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 .

Answer 2

We know:

• P($x$)={$x²$-(a+b)$x$+a+b}

$\dashrightarrow$Sum(a+b)=9

$\dashrightarrow$ product(ab)=18

Now Putting the values,

$\dashrightarrow${$x²$-(9)$x$+18}

$\dashrightarrow$$x²$-9$x$+18

$\dashrightarrow$$x²$+6$x$-3$x$+18

$\dashrightarrow$$x$($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.