Find the quadratic polynomial whose zeros are 2 and -1/3?

Question

Answer

Answer

As we know, quadratic formula =x^2-(alpha+beeta)x +alpha. beeta

Alpha= 2
Beeta = - 1/3

Sum of zeros = 2+(-1/3)
= 2-1/3
= 5/3

Product of zeros = 2*(-1/3)
- 2/3

Quadratic polynomial = x^2- 5x/3 - 2/3
= 3x^2- 5x - 2 is your answer

Answer

Answer

Zeroes=2and -1/3,
sum of zeros=2-1/3=5/3
product of the zeros=-2/3,

p(x)=x^2-( sum of zeros)x+ product of zeros,
or, p(x)=x^2-(5/3)x+(-2/3)=0,
x^2-5/3x-2/3=0,

3x^2-5x-2/3=0,

hence p(x)=3x^2-5x-2

Answer

Finding the Quadratic Polynomial with Zeros 2 and -1/3

Introduction

To find the quadratic polynomial with zeros 2 and -1/3, we need to use the formula for finding the roots of a quadratic equation. Once we have the roots, we can use the zero product property to find the quadratic polynomial.

Formula for Finding Roots of a Quadratic Equation

The formula for finding the roots of a quadratic equation is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation in the form of ax² + bx + c = 0.

Finding the Coefficients of the Quadratic Equation

To find the coefficients of the quadratic equation with roots 2 and -1/3, we need to use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients.

The sum of the roots is given by:

sum of roots = -b/a

And the product of the roots is given by:

product of roots = c/a

Substituting the values of the roots in the above equations, we get:

2 + (-1/3) = -b/a

6/3 - 1/3 = -b/a

5/3 = -b/a

Also,

2 * (-1/3) = c/a

-2/3 = c/a

Solving these equations simultaneously, we get:

a = 3
b = -5
c = 2

Finding the Quadratic Polynomial

Now that we have the values of a, b, and c, we can write the quadratic polynomial in the form of ax² + bx + c = 0.

Substituting the values, we get:

3x² - 5x + 2 = 0

Therefore, the quadratic polynomial with zeros 2 and -1/3 is:

3x² - 5x + 2

Answer

Find a quadratic polynomial with zeroes  _2 and1/3

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