Question

Find the zeroes of the quadratic polynomial 4x2-1.

Answer 1

Answer:

Zeroes are 1 / 2 and - 1 / 2

Step-by-step explanation:

We have given  quadratic polynomial :

4 x² - 1

Rewrite as :

= > ( 2 x )² - ( 1 )²

Using identity :

a² - b² = ( a + b ) ( a - b )

= > ( 2 x )² - ( 1 )²

= > ( 2 x + 1 ) ( 2 x - 1 )

Now zeroes equating with zero :

2 x + 1 = 0

= > 2 x = - 1

= > x = - 1 / 2

OR

2 x - 1 = 0

= > 2 x = 1

= > x = 1 / 2

Hence we get required answer.

Answer 2

Question :-

Find the zeroes of the quadratic polynomial 4x2-1.

Identity used :-

${a}^{2} - {b}^{2} = (a + b)(a - b)$

Solution :-

$\rightarrow4 {x}^{2} - 1 =0 \\ \\ \rightarrow{(2x)}^{2} - {1}^{2} = 0 \\ \\ \rightarrow \: (2x - 1)(2x + 1) = 0 \\ \\ \rightarrow2x - 1 = 0 \: and \: 2x + 1 = 0 \\ \\ \rightarrow \: 2x = 1 \: and \: 2x = - 1 \\ \\ \rightarrow \: x = \frac{1}{2} \: and \: x = \frac{ - 1}{2} \\ \\ {\red{\boxed{\mid{\bold{zeroes \:of \: polynomial \: are \: \frac{1}{2} \: and \: \frac{ - 1}{2} }}}}}$