Question

the quadratic polynomial whose zeroes are 0 and √2​

Answer 1

Step-by-step explanation:

sum of zeroes = 0+√2

= √2

product of zeroes = (0)(√2)

= 0

k[x²-(sum of zeroes)x+ ( product of zeroes)]

K[x²-√2x+0]

k[x²-√2x]

for k= 1

1[x²-√2x]

x²-√2x

Answer 2

Answer:

The correct answer will be -

$x^2 + \sqrt{2} x$

Step-by-step explanation:

Method I -

The sum of the roots = $0+\sqrt{2}= \sqrt{2}$

The product of roots = $0\times \sqrt{2} =0$

We know that a quadratic polynomial can be written as a relation between the sum of roots and the product of roots like this -

x^2 - (sum of the roots) x +(prod. of roots)

So,

$x^2 + \sqrt{2} x$ will be our polynomial.

Method II -

We know the roots of the polynomial so we can write it as the factor of the polynomial.

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

This will be our polynomial.

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