If $3$ and $-6$ as the sum and product of its zeros respectively, then write the quadratic polynomial $f( x)$.
Given: $3$ and $-6$ as the sum and product of its zeros respectively.
To do: To write the quadratic polynomial $f( x)$.
Solution:
Let $\alpha$ and $\beta$ be the zeros of the quadratic polynomial, then
$( \alpha+\beta)=3$
$\alpha\beta=-6$
The required polynomial will be
$f( x)=x^2-( \alpha+\beta)x+\alpha\beta$
$f( x)=x^2-3x-6$
Related Articles
- Form a quadratic polynomial $p( x)$ with $3$ and $\frac{2}{5}$ as sum and product of its zeroes, respectively.
- Find the polynomial, if the sum and the product of whose zeros are $-3$ and $2$ respectively.
- Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, $-$1 and $-$3 respectively.
- If the sum of the zeros of a polynomial is 2 and the product of zeros is 3 respectively. Find the equation.
- Find the polynomial whose sum and product of the zeros are $\frac{2}{3}$ and $\frac{5}{3}$ respectively.
- If $α$ and $β$ are the zeros of the quadratic polynomial $f(x)\ =\ ax^2\ +\ bx\ +\ c$, then evaluate: $α\ -\ β$.
- Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:$f(x)\ =\ x^2\ –\ (\sqrt{3}\ +\ 1)x\ +\ \sqrt{3}$
- If $α$ and $β$ are the zeros of the quadratic polynomial $f(x)\ =\ x^2\ -\ 1$, find a quadratic polynomial whose zeros are $\frac{2α}{β}$ and $\frac{2β}{α}$.
- For the following, find a quadratic polynomial whose sum and product respectively of the zeros are as given. Also, find the zeros of these polynomials by factorization.$-\frac{8}{3},\ \frac{4}{3}$
- Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:$f(x)\ =\ 6x^2\ –\ 3\ –\ 7x$
- Find a quadratic polynomial with the given numbers as the sum and product of zeroes respectively: $\sqrt{2},\ \frac{1}{3}$.
- If $α$ and $β$ are the zeros of the quadratic polynomial $f(x)\ =\ ax^2\ +\ bx\ +\ c$, then evaluate: $α^2β\ +\ αβ^2$
- If $α$ and $β$ are the zeros of the quadratic polynomial $f(x)\ =\ ax^2\ +\ bx\ +\ c$, then evaluate: $α^4\ +\ β^4$
- Find a quadratic polynomial with the given numbers as the sum and product of zeroes respectively: $1,\ 1$.
- Find a quadratic polynomial with the given numbers as the sum and product of zeroes respectively: $4,\ 1$
Kickstart Your Career
Get certified by completing the course
Get Started