Question

verify the relationship between the zeroes and the coefficient 4u²+8u​

Answer 1

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Let f(u)=4u

2

+8u

To calculate the zeros of the given equation, put f(u)=0.

4u

2

+8u=0

4u(u+2)=0

u=0,u=−2

The zeros of the given equation is 0 and −2.

Sum of the zeros is 0+(−2)=−2.

Product of the zeros is 0×−2=0.

According to the given equation,

The sum of the zeros is,

a

−b

=

4

−(8)

=−2

The product of the zeros is,

a

c

=

4

0

=0

Hence, it is verified that,

sumofzeros=

coefficientofx

2

−coefficientofx

And,

productofzeros=

coefficientofx

2

constantterm

Answer 2

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$Let f(u)=4u2+8u</p><p></p><p>To calculate the zeros of the given equation, put f(u)=0.</p><p></p><p>4u2+8u=0</p><p></p><p>4u(u+2)=0</p><p></p><p>u=0,u=−2</p><p></p><p>$

$The \: zeros \: of \: the \: given \: equation \: is 0 and −2.</p><p></p><p>Sum \: of \: the \: zeros \: is  \: 0+(−2)=−2.</p><p></p><p>Product \: of \: the \: zeros \: is 0×−2=0.</p><p></p><p>According \: to \: the \: given \: equation,</p><p></p><p>The \: sum \: of \: the \: zeros \: is,</p><p></p><p>$

$a−b=4−(8)</p><p></p><p>=−2</p><p></p><p>The \: product \: of \: the \: zeros \: is,</p><p></p><p>ac=40</p><p></p><p>=0</p><p></p><p>Hence, \: it \: is \: verified \: that,</p><p></p><p>$

$sum \: of \: zeros \: = \binom{ - coefficientofx}{</p><p>coefficientofx2−} </p><p></p><p></p><p>$

$roductofzeros=coefficientofx2constantterm</p><p></p><p></p><p>$