Question

find the quadratic polynomial, the Sum & product of
whoes - Zeroes are - 3 & 2. respectively. H.​

Answer 1

EXPLANATION.

Quadratic polynomial whose sum of zeroes = -3.

Quadratic polynomial whose products of zeroes = 2.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -3.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = 2.

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation.

⇒ x² - (-3)x + (2) = 0.

⇒ x² + 3x + 2 = 0.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

Answer:

Given :-

Sum of zeroes = -3

Product of zeroes = 2

To Find :-

Quadratic polynomial

Solution :-

We have

$\begin{cases} \sf \: \alpha + \beta = \frak{ - 3} \\ \sf \: \alpha \beta = \frak{2} \end {cases}$

General form of Quadratic polynomial

$\sf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

x² - (-3)x + 2

x² + 3x + 2