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Find the quadratic polynomial, sum of whose zeroes is 0 and th

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Find the quadratic polynomial, sum of whose zeroes is $0$ and their product is $- 1.$ Hence find the zeroes of the polynomial.

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Theodore Discussed

Find the quadratic polynomial, sum of whose zeroes is

0

and their product is

- 1.

Hence find the zeroes of the polynomial.

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Given : Sum fo zeroes =

(α + β) = 0

Product of the zeroes =

α β = - 1

Required quadratic polynomial is

x^{2} - (α + β) x + α β = x^{2} - (0) x - 1

= x^{2} - 1

Now, find the zeroes of the above polynomial.
Let

f (x) = x^{2} - 1

x^{2} - 1^{2}

(x - 1) (x + 1)

Substitute

f (x) = 0

(x - 1) = 0

(x + 1) = 0

\Rightarrow x = 1

x = - 1

1

and

- 1

are the zeroes of the polynomial.

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Question Text	Find the quadratic polynomial, sum of whose zeroes is $0$ and their product is $- 1.$ Hence find the zeroes of the polynomial.
Answer Type	Text solution:1
Upvotes	150