Question

Find a quadratic polynomial, the sum and product of whose zeroes are 5 and 3 respectively.​

Answer 1

Answer:

x^2 - 8x + 15

Step-by-step explanation:

a+b = 8

ab = 15

General formula of quadratic equations is x^2 -(a+b)x + ab

Answer 2

$\underline\mathtt{Question:}$

Find a quadratic polynomial, the sum and product of whose zeroes are 5 and 3 respectively.

$\underline\mathtt{Answer:}$

Given the sum and product of the zeroes are 5 and 3

Let the zeroes be alpha and beta,

$\alpha + \beta = 5$ ; $\alpha \beta = 3$

To find a polynomial from the zeroes given we use,

$p_{(x)} = k[ {x}^{2} - ( \alpha + \beta)x + \alpha \beta ]$

$k[ {x}^{2} - 5x + 3 ]$

Here k is a constant and can be any number. Let's consider k = 1

Therefore the quadratic polynomial would be

$p_{(x)} = {x}^{2} - 5x + 3$

Have a good night!