Find a quadratic polynomial,sum and product of whose zeroes are -3 and 2 respectively?

Question

Answer

Quadratic polynomial = x^2 - ( sum of zeroes )*x + product of zeroes
x^2 - ( - 3 ) * x + 2
x^2 + 3x + 2

Answer

S= -3
P=2
f(x)= x^2-(S)x+P
=x^2+3x+2

Answer

Answer

Using the standard equation, x^2-Sx+P [ S for sum of zeroes ; P for product of zeroes], we get the answer as, x^2+3x+2 ( since the sum and product of the zeroes are -3 & 2 respectively) ..This is the simplest way to get a Q.E when sum & product are given for zeroes...hope it helped u :D

Answer

X2-(alpha +beta)x+(alpha × beta )
By this you get- x2+3x+2 and this is your answer.

Answer

We know
sum of zeros= -3
product of zeros= 2

we know a formula
x2-(sum of seros) x+ ( product of zeros)
x2 -(-3)x+2
x2 +3x + 2 is a quadratic polynomial

Answer

Understanding Quadratic Polynomials
A quadratic polynomial can be expressed in the standard form:
$$ P(x) = ax^2 + bx + c $$
Where $ a $, $ b $, and $ c $ are constants.

Sum and Product of Zeroes
For a quadratic polynomial $ ax^2 + bx + c $:
- The sum of the roots (zeroes) is given by:
$$ \text{Sum} = -\frac{b}{a} $$
- The product of the roots is given by:
$$ \text{Product} = \frac{c}{a} $$
Given that the sum of the zeroes is $-3$ and the product is $2$, we can denote the roots as $ \alpha $ and $ \beta $:
- $ \alpha + \beta = -3 $
- $ \alpha \cdot \beta = 2 $

Constructing the Polynomial
To find the quadratic polynomial, we can use the relationships between the coefficients and the roots:
1. **Using the sum and product**:
The polynomial can be expressed as:
$$ P(x) = a(x^2 - (\alpha + \beta)x + \alpha \cdot \beta) $$
2. **Substituting the values**:
$$ P(x) = a(x^2 - (-3)x + 2) $$
$$ P(x) = a(x^2 + 3x + 2) $$
3. **Choosing $ a = 1 $** (for simplicity):
$$ P(x) = x^2 + 3x + 2 $$

Final Result
Hence, the quadratic polynomial whose sum of zeroes is $-3$ and product is $2$ is:
$$ P(x) = x^2 + 3x + 2 $$
This polynomial has the required properties and can be verified by factoring or using the quadratic formula.

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