Find a quadratic polynomial .the sum of product of whose zeroes are -3 and 2. Respectively.?

Question

Answer

Answer

Alpha + beta = -3 = -b/a

alpha x beta = 2 = c/a

if a = 1, then b = 3, c = 2

quadratic equation is x2 + 3x + 2.

you can check by solving the above equation

Answer

Sum of zeroes = α + β  -3
Product of zeroes =  αβ = 2

a quadratic polynomial is given by :-

x² - [  α + β ]x + [ αβ ]
x² + 3x + 2  is the required polynomial

Answer

Introduction:
In this problem, we need to find a quadratic polynomial whose zeroes are -3 and 2. We know that the sum of the product of the zeroes of a quadratic polynomial is equal to the coefficient of x^2 divided by its leading coefficient.

Step 1: Finding the sum of the product of the zeroes:
Let's find the sum of the product of the zeroes of the quadratic polynomial.
Product of zeroes = -3 x 2 = -6
Sum of product of zeroes = -6

Step 2: Writing the quadratic polynomial:
Now, we can write the quadratic polynomial using the zeroes and the sum of the product of the zeroes.
Let the quadratic polynomial be ax^2 + bx + c
The zeroes of the polynomial are -3 and 2
Sum of product of zeroes = -6

We know that the sum of the product of the zeroes of a quadratic polynomial is equal to the coefficient of x^2 divided by its leading coefficient. Therefore,
a = (-6)/1 = -6

So, the quadratic polynomial is -6x^2 + bx + c

Step 3: Finding the coefficients:
To find the values of b and c, we can use the fact that the quadratic polynomial has -3 and 2 as its zeroes. We know that if a quadratic polynomial has zeroes p and q, then (x-p)(x-q) is a factor of the polynomial. Therefore,
(x-(-3))(x-2) = (x+3)(x-2) is a factor of the polynomial.

Expanding (x+3)(x-2), we get
x^2 + x - 6

Comparing this with -6x^2 + bx + c, we get
b = 1 and c = -6

Step 4: Writing the final quadratic polynomial:
Therefore, the final quadratic polynomial is
-6x^2 + x - 6

Conclusion:
In this problem, we found a quadratic polynomial whose zeroes are -3 and 2 and whose sum of product of zeroes is -6. We used the fact that the sum of product of zeroes of a quadratic polynomial is equal to the coefficient of x^2 divided by its leading coefficient, and the fact that the polynomial can be written as (x-p)(x-q) if it has zeroes p and q. We then found the values of b and c by expanding (x-p)(x-q) and comparing it with the given quadratic polynomial.

Answer

We know
sum of zeros = (alpha +beta)= -3
product of zeros= ( alpha ×beta)= 2

we know a formula
x2-( alpha + beta)x +(alpha × beta)
x2 -(-3)x+ 2
x2 +3x +2is the quadratic polynomial

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