Question

How to solve this equation as the question is verify if the fault in our zero of polynomial I want it solved by step-by-step not in one word answer in full explanation

Answer 1

Question :

Verify Whether the following are zeros of the polynomial.

i) p( x ) = x² , x = 0.

ii) p( x ) 3x² - 1 , - 1/√3 , 2/√3.

Solution :

Q. What do you mean of Zeros of polynomial p( x ) ?

• When we Putting the value with respect to x they should becoming 0. It consider as Zeros of polynomial or P( x )

$\rule{90}1$

i) p( x ) = x² , x = 0.

Putting the value 0.

$\tt \longmapsto {x}^{2}$

$\tt \longrightarrow {0}^{2}$

$\tt \longrightarrow 0.$

Yes, It zeros of P( x )

$\rule{90}1$

ii) P( x ) = 3x² - 1.

$\tt \longrightarrow 3 {x}^{2} - 1$

When, x = -1 /√3.

$\tt \longrightarrow 3 { (\dfrac{ - 1}{ \sqrt{3} } )}^{2}$

$\tt \longrightarrow 3 \times \dfrac{1}{3}$

$\tt \longrightarrow 1 - 1$

$\tt \longrightarrow 0.$

Yes, It zeros of P( x )

$\rule{90}1$

When, x= 2 /√3.

$\tt \longrightarrow 3 {x}^{2} - 1$

$\tt \longrightarrow 3 \times {(\dfrac{2}{ \sqrt{3} } ) }^{2} - 1$

$\tt \longrightarrow 3 \times \dfrac{4}{3} - 1$

$\tt \longrightarrow 4 - 1$

$\tt \longrightarrow 3.$

No, It have not Zeros of given P( x )