Question

HEYA MATE....

UR Question: 16
If α and β are the zeroes of the quadratic polynomial such that α + β = 24 and α – β = 8, find a quadratic polynomial having α and β as its zeroes.​

Answer 1

Answer:

The required polynomial is P(x)=x^2-24x+128P(x)=x

2

−24x+128 .

Step-by-step explanation:

It is given that α and β are the zeros of a quadratic polynomial such that

\alpha +\beta =24α+β=24 .... (1)

\alpha -\beta =8α−β=8 .... (2)

Add both the equations.

2\alpha=322α=32

\alpha=16α=16

Put this value in equation (1).

16+\beta =2416+β=24

\beta =8β=8

The value of α and β are 16 and 8 respectively.

If α and β are the zeros of a quadratic polynomial, the polynomial is in the form of

P(x)=x^2-(\alpha +\beta)x+\alpha \betaP(x)=x

2

−(α+β)x+αβ

P(x)=x^2-(24)x+16 \times 8P(x)=x

2

−(24)x+16×8

P(x)=x^2-24x+128P(x)=x

2

−24x+128

Therefore, the required polynomial is P(x)=x^2-24x+128P(x)=x

2

−24x+128 .