If alpha and beta are the zeros of polynomial

Asked by admin @ 11/08/2021 in Math viewed by 326 People

if alpha and beta are the zeros of a quadratic polynomial such that alpha + beta is equals to 24 and Alpha minus beta is equal to 8 find the quadratic polynomial having alpha and beta as its zeros verify the relationship between zeroes and coefficients of the polynomial

Answered by admin @ 11/08/2021

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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