Question

write a quadratic polynomial sum of whose zeroes is 3 and product is 2​

Answer 1

Answer:

x  ^ 2

−3x+2

Step-by-step explanation:

α+β=3,αβ=2

Quadratic polynomial:

x  ^2

−(α+β)x+(αβ)

∴ Polynomial is x  ^2

−3x+2

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Answer 2

EXPLANATION.

Quadratic polynomial whose sum is = 3.

Quadratic polynomial whose product is = 2.

As we know that,

Sum of zeroes of quadratic equation,

⇒ α + β = -b/a.

⇒ α + β = 3.

Products of zeroes of quadratic equation,

⇒ αβ = c/a.

⇒ αβ = 2.

Equation of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in this equation, we get.

⇒ x² - (3)x + 2 = 0.

⇒ x² - 3x + 2 = 0.

                                                                                                                         

MORE INFORMATION.

Nature of the factors 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.