Math, asked by BhavyamRajguru, 2 months ago

Find the zeroes of the polynomial.x2-3 and verify the relationship between the zeroes and the coefficients.​

Answers

Answered by tennetiraj86
2

Step-by-step explanation:

Given :-

The polynomial is X²-3

To find :-

Find the zeroes of the polynomial x²-3 and verify the relationship between the zeroes and the coefficients.?

Solution :-

Given that

The quardratic polynomial P(x) = X²-3

Finding the zeroes :-

To get zeroes of P(x) then we equate P(x) to zero

=> P(x) = 0

=> X²-3 = 0

=> X²-(√3)² = 0

=> (X+√3)(X-√3) = 0

Since, (a+b)(a-b) = a²-b²

Where, a = X and b = √3

=> X+√3 = 0 (or) X-√3 = 0

=> X = -√3 (or) X = √3

The zeroes are √3 and -√3

Verifying the relationship between the zeroes and the coefficients :-

Given quardratic polynomial P(x) = X²-3

On comparing with the standard quadratic polynomial ax²+bx+c then

a = 1

b = 0

c = -3

Zeroes are √3 and -√3

Sum of the zeroes = √3+(-√3)

=> (√3-√3)

=> 0

=> -(Coefficient of x)/Coefficient of x²

=> -(0)/1

=> 0/1

=> 0

=> -b/a

Sum of the zeroes = -b/a

Product of the zeroes = (√3)(-√3)

=> -[√(3×3)]

=> -√9

=> -3

=> Constant term / Coefficient of x²

=> c/a

Product of the zeroes = c/a

Verified.

Used formulae:-

→ The standard quadratic Polynomial is ax²+bx+c

→ Sum of the zeroes = -b/a

→ Product of the zeroes = c/a

→ (a+b)(a-b) = a²-b²

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