Question

Find a quadratic polynomial whose zeros are 1/root 2 and 1/-root2

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Answer 1

Answer:

P(x) = 2x² - 1

Step-by-step explanation:

Find a quadratic polynomial whose zeros are 1/root 2 and 1/-root2

Zeroes are 1/√2   &  -1/√2

Polynomial

( x - 1/√2)(x - (-1/√2)

= ( x - 1/√2)(x + 1/√2)

= x²  - 1/2

Multiplying by 2

= 2x² - 1

P(x) = 2x² - 1

Answer 2

Solution:

Let m,n are two zeroes of

quadratic polynomial.

m=1/√2 , n = -1/√2

i)Sum of the zeroes = m+n

= 1/√2 + (-1/√2)

= 0

ii) product of the roots = mn

= (1/√2)(-1/√2)

= -1/2

/* We know that ,

Form of Quadratic expression whose zeroes are m,n is

-1k[x²-(m+n)x+mn] */ ,

Now,

k[x²-0*x+(-1/2)]

= k[x²-1/2]

For all real values of k it is true.

Let k = 2,

The polynomial is

= 2x²-1

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