Question

if alpha beta are the zeroes of the polynomial such that alpha + beta = 6 and alpha beta = 4 . write the polynomial​

Answer 1

Solution:

We have been given α and β are the zeroes of the polynomial such that α + β= 6 and αβ = 4 .

Sum of Zeroes:

α + β= 6

Product of Zeroes :

αβ = 4

General Formula of Quadratic Polynomial:

f(x) = x² - ( α + β )x + αβ

Find the Quadratic Polynomial:

x² - ( α + β )x + αβ

x² - ( 6 )x + 4

x² - 6x + 4

Therefore, Required Polynomial will be x² - 6x + 4.

Answer 2

Answer:

$x^{2} - 6x + 4 = 0$

Step-by-step explanation:

Given:- α and β are the zeroes of the polynomial such that α+β = 6 and

            αβ = 4.

To Find:- The Required polynomial whose zeroes are α and β.

Solution:-

Given α + β = 6 and αβ = 4

A polynomial is an expression which consists of variables, exponents, terms and constants.  

Since the polynomial has two zeroes, so it is a quadratic polynomial whose degree is 2.

General Equation of a Quadratic equation is:

                                 $x^{2}$ - ( α + β )$x$ + αβ = 0

Now, putting the values in the above equation, it becomes

                                     $x^{2} - 6x + 4 = 0$

Therefore, the polynomial with zeroes α and β is $x^{2} - 6x + 4 = 0$.

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