Question

sum and product of zeros of quadratic polynomial are 5 and 17 respectively find the polynomial

Answer 1

The required quadratic polynomial is $x^{2} -5x+17$.

Step-by-step explanation:

We are given that sum and product of zeros of a quadratic polynomial are 5 and 17 respectively.

Let the required quadratic polynomial be of the form $ax^{2} +bx+c$ ; where a, b, and c are constants.

Now, as we know that the sum of the zeroes of a quadratic polynomial is given by;

$\alpha + \beta=\frac{-b}{a}$

 $5 = \frac{-b}{a}$

Assuming a = 1, we get b = -5.

Similarly, the product of the zeroes of a quadratic polynomial is given by;

$\alpha \times \beta=\frac{c}{a}$

 $17 = \frac{c}{a}$

Assuming a = 1, we get c = 17.

So, the required quadratic polynomial will be $x^{2} -5x+17$.

Answer 2

Answer:

The required quadratic polynomial is x^{2} -5x+17x

2

−5x+17 .

Step-by-step explanation:

We are given that sum and product of zeros of a quadratic polynomial are 5 and 17 respectively.

Let the required quadratic polynomial be of the form ax^{2} +bx+cax

2

+bx+c ; where a, b, and c are constants.

Now, as we know that the sum of the zeroes of a quadratic polynomial is given by;

\alpha + \beta=\frac{-b}{a}α+β=

a

−b

5 = \frac{-b}{a}5=

a

−b

Assuming a = 1, we get b = -5.

Similarly, the product of the zeroes of a quadratic polynomial is given by;

\alpha \times \beta=\frac{c}{a}α×β=

a

c

17 = \frac{c}{a}17=

a

c

Assuming a = 1, we get c = 17.

So, the required quadratic polynomial will be x^{2} -5x+17x

2

−5x+17 .