Find the quadratic polynomial whose zeroes are $-2$ and $-5$.
Given: Zeroes of the quadratic polynomial are $-2$ and $-5$.
To do: To find the polynomial.
Solution:
As given, zeroes of the quadratic polynomial are $-2$ and $-5$.
Therefore, Sum of the zeroes $\alpha+\beta=-2+( -5)=-7$
Product of the zeroes $\alpha\beta=( -2)\times ( -5)=10$
Thus, the polynomial is : $x^2-( \alpha+\beta)x+\alpha\beta=0$
$\Rightarrow x^2-( -7)x+10=0$
$\Rightarrow x^2+7x+10=0$
Therefore, the polynomial is $x^2+7x+10=0$.
Related Articles
- Write a quadratic polynomial, whose zeroes are $-4$ and $-5$.
- Find a quadratic polynomial whose zeroes are $\frac{3+\sqrt{5}}{5}$ and $\frac{3-\sqrt{5}}{5}$.
- Find a quadratic polynomial, the sum and product of whose zeroes are $0$ and $-\frac{3}{5}$ respectively. Hence find the zeroes.
- Form a quadratic polynomial whose zeroes are $3+\sqrt{2}$ and $ 3-\sqrt{2}$.
- If $\alpha$ and $\beta$ are zeroes of a quadratic polynomial $4x^{2}+4x+1=0$, then form a quadratic polynomial whose zeroes are $2\alpha$ and $2\beta$.
- if $\alpha$ and $\beta$ are zeroes of polynomial $x^{2}-2x-15$, then form a quadratic polynomial whose zeroes are $2\alpha$ and $2\beta$.
- Find a quadratic polynomial, the sum and product of whose zeroes are $-8$ and $12$ respectively. Hence find the zeroes.
- Find a quadratic polynomial , the sum and product of whose zeroes are $\sqrt{3}$ and $\frac{1}{\sqrt{3}}$.
- Find the zeroes of the quadratic polynomial $6x^2-3-7x$ and verify the relationship between the zeroes and the coefficients of the polynomial.
- Find the zeroes of the quadratic polynomial $3x^{2}-75$ and verify the relationship between the zeroes and the coefficients.
- Find, whether the zeroes of the quadratic polynomial $x^2+99x+127$ are positive or negative.
- Find the zeroes of the quadratic polynomial $f( x)=x^2-3x-28$.
- Write the Polynomial whose zeroes are $\sqrt{\frac{3}{2}}, -\sqrt{\frac{3}{2}}$.
- If $α$ and $β$ are the zeros of the quadratic polynomial $f(x)\ =\ x^2\ -\ 2x\ +\ 3$, find a polynomial whose roots are $α\ +\ 2,\ β\ +\ 2$.
- 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 $\frac{2β}{α}$.
Kickstart Your Career
Get certified by completing the course
Get Started