Question

Find a quadratic polynomial each with the given numbers as the sum and

product of its zeroes respectively root 3 and -root 3​

Answer 1

EXPLANATION.

Sum of its zeroes = √3.

Products of its zeroes = -√3.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ α + β = √3. - - - - - (1).

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = -√3. - - - - - (2).

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (√3)x + (-√3).

⇒ x² - √3x - √3.

                                                                                                                         

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

Answer:

x^2-√3x-√3

Step-by-step explanation:

any quadratic equation is of the form

x^2-(sum of zeros)x+product of zeros

here

x^2-(√3)x+(-√3)

=x^2-√3x-√3