Question

Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2, respectively.​

Answer 1

Step-by-step explanation:

Given

α+β=

8

21

and

αβ=

16

5

∴f(x)=x

2

−(α+β)x+αβ

⇒f(x)=x

2

−(

8

21

)+(

16

5

)

Multiplying (or dividing) f(x) by any real number does not affect the zeroes of f(x) So, multiplying f(x) by 16 (LCM), we get

f(x)=16x

2

−42x+5

For zeroes of polynomial f(x),

f(x)=0

⇒16x

2

−42x+5=0

⇒16x

2

−40x−2x+5=0

⇒8x(2x−5)−1(2x−5)=0

⇒(2x−5)(8x−1)=0

⇒2x−5=0 or 8x−1=0

⇒x=

2

5

or x=

8

1

∴α=

2

5

and β=

8

1

hope it is helpfull army.