Question

Find the quadratic polynomial whose zeroes are root 3+root 5 and root 5 - root 3

Answer 1

quadratic polynomial =ax^2+bx+c
where c=product of there roots
& b=sum of there roots.
quadratic polynomial =

x^2-(root3+root5+root5-root3)x+(root3+root5)(root5-root3)
x^2-2root5x+16.

pls mark as brainliest.

Answer 2

Concept:

In algebra, a form known with one or more variables in which the greatest term is of the second degree is known as a quadratic function, a quadratic polynomial, a linear function of degree 2, or simply a quadratic.

Given:

What quadratic polynomials has roots with zeros 3+√5 and 3-√5

Find:

explore the response to the posed question.

Answer:

A polynomials of degree two, or one in which two is the highest exponent of the variable, is a cubic quadratic. y = ax2 + bx + c is the formula for a quadratic polynomial graph. The values of y can be calculated by changing the value of x in this equation. A quadratic function has the conventional form ax2+bx+c=0, where a, b, and c are real values and a0. The coefficient of x2 is "a." The quadratic coefficient is what it is termed.

let

$\alpha =3+\sqrt{5}$

$\beta =3-\sqrt{5}$

sum of zeroes $=\alpha +\beta$

                        $=3+\sqrt{5} +3-\sqrt{5}$

                        $=6$

product of zeroes $=\alpha \beta$

                              $=(3+\sqrt{5} )(3-\sqrt{5} )$

                               $=9-5$

                               $=4$

sum of roots $=-\frac{b}{a}$

                     $=-\frac{6}{1}$

product of roots $=\frac{c}{a}$

                           $=\frac{4}{1}$

$a = 1\\b = -6\\c = 4$

therefore the quadratic polynomial is $x^{2} -6x+4$

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