Question

6. Find the quadratic polynomial, the sum of whose zeros is O and their product is -1.
Hence find the zeros of the polynomial.​

Answer 1

Answer:

p(x)= x² -1

1 and -1

☸Given☸

Sum of Zeroes= 0

Product of Zeroes = -1

To Find:

➺ A quadratic polynomial sum of whose zeroes is 0 and their product is -1

$\rule{300}{2}$

✺Solution✺

We know that,

A quadratic polynomial is expressed in the form of:

p(x)=x² - (Sum of Zeroes)+(Product of Zeroes)

where, x is a variable

So, required polynomial is

☛ p(x)= x² -(0)+(-1)

☛ p(x)= x² -1

$\rule{300}{2}$

Since, it is a quadratic polynomial, it will have two zeroes

Let one of the zeroes be α

Then, α will satisfy the polynomial or when we put α in the polynomial, we will will get final value as 0

i.e. p(α)=0

➳ α² -1= 0

➳ (α+1)(α-1)=0

[Since, a²-b²=(a+b)(a-b)]

➳ α+1=0   ,    α-1=0

➳ α=1,-1

So, 1 and -1 are the required zeroes.

Hence, the required polynomial is

p(x)= x²-1 whose zeroes are 1 and -1.

Answer 2

Answer:

p(x)= x² -1

1 and -1

☸Given☸

Sum of Zeroes= 0

Product of Zeroes = -1

To Find:

➺ A quadratic polynomial sum of whose zeroes is 0 and their product is -1

✺Solution✺

We know that,

A quadratic polynomial is expressed in the form of:

p(x)=x² - (Sum of Zeroes)+(Product of Zeroes)

where, x is a variable

So, required polynomial is

☛ p(x)= x² -(0)+(-1)

☛ p(x)= x² -1

Since, it is a quadratic polynomial, it will have two zeroes

Let one of the zeroes be α

Then, α will satisfy the polynomial or when we put α in the polynomial, we will will get final value as 0

i.e. p(α)=0

➳ α² -1= 0

➳ (α+1)(α-1)=0

[Since, a²-b²=(a+b)(a-b)]

➳ α+1=0   ,    α-1=0

➳ α=1,-1

So, 1 and -1 are the required zeroes.

Hence, the required polynomial is

p(x)= x²-1 whose zeroes are 1 and -1.

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