2 thoughts on “• Class – 10 •<br /><br />
Find the quadratic polynomials whose zeroes are <br />
3 ± √2”
Step-by-step explanation:
Answer: p(x) = x² – 6x + 7
Given the zeroes of a quadratic polynomials as:
3 + √2
3 – √2
We know, when the coefficient of x² is 1 then the coefficient of x is negative of the sum of the zeroes while the constant term is the product of the zeroes. Which is given by:
p(x) = x² – (Sum of zeroes)x + Product of zeroes
Now, Let’s find the sum and product of the zeroes,
⇒ Sum of zeroes = (3 + √2) + (3 – √2)
⇒ Sum of zeroes = 3 + √2 + 3 – √2
⇒ Sum of zeroes = 3 + 3
⇒ Sum of zeroes = 6
Further, Let’s find the product of zeroes,
⇒ Product of zeroes = (3 + √2)(3 – √2)
⇒ Product of zeroes = (3)² – (√2)²
As,
(a + b)(a – b) = a² – b²
⇒ Product of zeroes = 9 – 2
⇒ Product of zeroes = 7
Now that we have got the sum and the product of the zeroes let’s substitute them in the formula discussed earlier.
⇒ p(x) = x² – 6x + 7 = 0
Hence, It is the required polynomial.
Some Information :-
We can find the zeroes of a quadratic polynomial using the quadratic formula where a, b and c are given by
We know, when the coefficient of x² is 1 then the coefficient of x is negative of the sum of the zeroes while the constant term is the product of the zeroes. Which is given by:
p(x)=x²–(Sumofzeroes)x+Productofzeroes
Now, Let’s find the sum and product of the zeroes,
⇒ Sum of zeroes = (3 + √2) + (3 – √2)
⇒ Sum of zeroes = 3 + √2 + 3 – √2
⇒ Sum of zeroes = 3 + 3
⇒ Sumofzeroes=6
Further, Let’s find the product of zeroes,
⇒ Product of zeroes = (3 + √2)(3 – √2)
⇒ Product of zeroes = (3)² – (√2)²
As,
(a + b)(a – b) = a² – b²
⇒ Product of zeroes = 9 – 2
⇒ Productofzeroes=7
Now that we have got the sum and the product of the zeroes let’s substitute them in the formula discussed earlier.
⇒ p(x) = x² – 6x + 7 = 0
Hence,Itistherequiredpolynomial.
SomeInformation:–
We can find the zeroes of a quadratic polynomial using the quadratic formula where a, b and c are given by
Step-by-step explanation:
Answer: p(x) = x² – 6x + 7
Given the zeroes of a quadratic polynomials as:
3 + √2
3 – √2
We know, when the coefficient of x² is 1 then the coefficient of x is negative of the sum of the zeroes while the constant term is the product of the zeroes. Which is given by:
p(x) = x² – (Sum of zeroes)x + Product of zeroes
Now, Let’s find the sum and product of the zeroes,
⇒ Sum of zeroes = (3 + √2) + (3 – √2)
⇒ Sum of zeroes = 3 + √2 + 3 – √2
⇒ Sum of zeroes = 3 + 3
⇒ Sum of zeroes = 6
Further, Let’s find the product of zeroes,
⇒ Product of zeroes = (3 + √2)(3 – √2)
⇒ Product of zeroes = (3)² – (√2)²
As,
(a + b)(a – b) = a² – b²
⇒ Product of zeroes = 9 – 2
⇒ Product of zeroes = 7
Now that we have got the sum and the product of the zeroes let’s substitute them in the formula discussed earlier.
⇒ p(x) = x² – 6x + 7 = 0
Hence, It is the required polynomial.
Some Information :-
We can find the zeroes of a quadratic polynomial using the quadratic formula where a, b and c are given by
a = Coefficient of x²
b = Coefficient of x
c = constant term
hope this helps you!!
thank you ⭐
Answer: p(x) = x² – 6x + 7
Given the zeroes of a quadratic polynomials as:
We know, when the coefficient of x² is 1 then the coefficient of x is negative of the sum of the zeroes while the constant term is the product of the zeroes. Which is given by:
Now, Let’s find the sum and product of the zeroes,
⇒ Sum of zeroes = (3 + √2) + (3 – √2)
⇒ Sum of zeroes = 3 + √2 + 3 – √2
⇒ Sum of zeroes = 3 + 3
⇒ Sum of zeroes = 6
Further, Let’s find the product of zeroes,
⇒ Product of zeroes = (3 + √2)(3 – √2)
⇒ Product of zeroes = (3)² – (√2)²
As,
⇒ Product of zeroes = 9 – 2
⇒ Product of zeroes = 7
Now that we have got the sum and the product of the zeroes let’s substitute them in the formula discussed earlier.
⇒ p(x) = x² – 6x + 7 = 0
Hence, It is the required polynomial.
Some Information :–