Question

A quadratic polynomial whose one zero is 6 and sum of zeroes is 0,is
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Answer 1

Given:

→One zero of a quadratic polynomial is 6 .

→Sum of zeroes is 0 .

To Find:

The quadratic polynomial according to the given data.

Answer:

Let us take

• $\sf{First\:zero\: as\:\alpha}$
• $\sf{Second\: zero\:as\:\beta}$

Now,

If one zero is 6 and sum of zeroes is 0.

So,

$\sf{\implies \alpha+\beta=0}$

$\sf{\implies 6+\beta=0}$

$\sf{\red{\leadsto \beta=-6}}$

Formula = p(x)=k[x²-(a+ß)+aß

=>p(x) =k[x²-(6-6)+(-6×6)].

=>p(x) =k[ x²-0+(-36)] .

.°. p(x) = k[x²-36]

Answer 2

Answer:

$k( {x}^{2} - 36)$

Step-by-step explanation:

Let another zero be 'm'

So, 6 + m = 0

=> m = -6

so, sum of the zeroes = 0

and product of the zeroes = 6 ×(-6) = -36

We know that a quadratic polynomial, the sum and product of whose zeroes are known, is given by

$k({x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes))$

where k is any constant.

So, The polynomial is

$k( {x}^{2} - (0)x + ( - 36)) \\ = > k( {x}^{2} - 36)$

Please mark it as brainliest.