Question

Find a quadratic polynomial the sum and product of whose zeros are 3 and 2 respectively

Answer 1

$\boxed{\boxed{SOLUTION}}$

GIVEN

$\alpha + \beta = 3$

$\alpha \beta = 2$

A quadratic equation is given by:-

x² - (α+β)x + αβ

So,

the formula is

x² - 3x + 2

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Answer 2

Answer: $(x^{2}-3x+2)$

Step-by-step explanation:

Let the zeroes of the quadratic polynomial be a and b respectively.

The general form of a quadratic equation is :

$ax^{2}+bx+c$

Given :

(a + b)=3

(ab)=2

To find: the quadratic polynomial

Calculation:

When zeroes of a quadratic polynomial is known, the polynomial can be written as :

$f(x)=k(x^{2}-sum\ of\ zeroes(x)+product\ of\ zeroes)$

$f(x)=K(x^{2}-3x+2)$

(where k is a real number)

Therefore the required quadratic polynomial is:

$(x^{2}-3x+2)$