Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=3 x^{2}-1,\,x=-\,\frac{1}{\sqrt{3}},\, \frac{2}{\sqrt{3}}$
Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=3 x^{2}-1,\,x=-\,\frac{1}{\sqrt{3}},\, \frac{2}{\sqrt{3}}$
If $x=\frac{-1}{\sqrt{3}}$ and $\sqrt{x=\frac{2}{\sqrt{3}}}$ are zeroes of polynomial $p ( x )=3 x ^{2}-1,$ then $p\left(\frac{-m}{l}\right)$
$p\left(\frac{-1}{\sqrt{3}}\right)$ and $p\left(\frac{2}{\sqrt{3}}\right)$ should be $0$
Here, $p\left(\frac{-1}{\sqrt{3}}\right)=3\left(\frac{-1}{\sqrt{3}}\right)^{2}-1=3\left(\frac{1}{3}\right)-1=1-1=0,$ and $p\left(\frac{2}{\sqrt{3}}\right)=3\left(\frac{2}{\sqrt{3}}\right)^{2}-1=3\left(\frac{4}{3}\right)-1=4-1=3$
Hence, $x=\frac{-1}{\sqrt{3}}$ is a zero of the given polynomial. However, $x=\frac{2}{\sqrt{3}}$ is not a zero of the given polynomial.
Similar Questions
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.
Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x+\pi$
Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x+\pi$
Check whether the polynomial $q(t)=4 t^{3}+4 t^{2}-t-1$ is a multiple of $2 t+1$.
Check whether the polynomial $q(t)=4 t^{3}+4 t^{2}-t-1$ is a multiple of $2 t+1$.
Factorise of the following : $8 a^{3}-b^{3}-12 a^{2} b+6 a b^{2}$
Factorise of the following : $8 a^{3}-b^{3}-12 a^{2} b+6 a b^{2}$
Expand each of the following, using suitable identities : $(x+2 y+4 z)^{2}$
Expand each of the following, using suitable identities : $(x+2 y+4 z)^{2}$