Question

find the sum of zeroes of polynomial 3x²-7

Answer 1

The given polynomial is 3x^2- 7

( 3x^2+0x-7)

a=3

b=0

c=(-7)

Sum of zeroes

@+B

= -b/a

= -coefficient of x/ coefficient of x^2

= -0/3

= 0

Answer 2

Answer:

Sum of zeroes of given polynomial is 0.

Step-by-step explanation:

Given polynomial is

$\: f(x) = 3 {x}^{2} - 7...........(1)$

Now,

$f(x) = 0$

$3 {x}^{2} - 7 = 0$

Dividing by 3 in both side,

$\frac{3 {x}^{2} }{3} - \frac{7}{3} = 0$

${x}^{2} - \frac{7}{3} = 0$

${x}^{2} - { (\frac{ \sqrt{7} }{ \sqrt{3} })}^{2} = 0$

We know,

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

Here,

$a = x \: \: \: and \: \: b = \frac{ \sqrt{7} }{ \sqrt{3} }$

So,

${x}^{2} - { (\frac{ \sqrt{7} }{ \sqrt{3} })}^{2} = (x - \frac{ \sqrt{7} }{ \sqrt{3}} )(x + \frac{ \sqrt{7} }{ \sqrt{3} } ) = 0$

We know if multiplication of two term is zero then they are separately zero.

$(x - \frac{ \sqrt{7} }{ \sqrt{3} } ) = 0$

$x = \frac{ \sqrt{7} }{ \sqrt{3} }$

And,

$(x + \frac{ \sqrt{7} }{ \sqrt{3} } ) = 0$

$x = - \frac{ \sqrt{7} }{ \sqrt{3} }$

Sum of zeros=

$\frac{ \sqrt{7} }{ \sqrt{3} } + ( - \frac{ \sqrt{7} }{ \sqrt{3} } )$

$\frac{ \sqrt{7} }{ \sqrt{3} } - \frac{ \sqrt{7} }{ \sqrt{3} } = 0$

Required sum is 0.