Question

If alpha and beta are the zeroes of a quadratic polynomial alpha+beta=24 and alpha-beta=17 such that Find the quadratic polynomial having alpha and beta as its zeroes. Verify the relationship between the zeroes and coefficients of the polynomial

Answer 1

Answer:

The required polynomial is P(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 =24 .... (1)

\alpha -\beta =8 .... (2)

Add both the equations.

2\alpha=32

\alpha=16

Put this value in equation (1).

16+\beta =24

\beta =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 \beta

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

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

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

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