Question

if a and b are zeroes of p(x) =x square -2x +1 them a square +b square ​

Answer 1

Value of “ α² + β² = 2 ”.

Step-by-step explanation:

★ Given that :

• α and β are the zeroes of the Quadratic Polynomial p(x) = x² - 2x + 1 = 0

★ To find :

• Value of α² + β².

★ Let :

◼ According to the general form of Quadratic Polynomial is : ax² + bx + c = 0

◼ Consider the given polynomial.

• a = 1
• b = - 2
• c = 1

➡ Sum of the zeroes : α + β = -b/a = -(-2)/1 = 2

➡ Product of the zeroes : αβ = c/a = 1/1 = 1

Now, we can find out the value of α² + β².

➠ α² + β² = (α + β)² - 2αβ

• Substitute the zeroes.

➠ α² + β² = (2)² - 2(1)

➠ α² + β² = 4 - 2

➠ α² + β² = 2

∴ The value of α² + β² is " 2 ".

Answer 2

Answer:

2

Step-by-step explanation:

IT IS GIVEN,

P(x)= x²-2x+1

a & b are zeroes of P(x)

PUTTING THE VALUE OF a IN P(X)

a²-2a+1=0. [ BY FACTOR THEOREM]

⇒(a-1)²=0

⇒a-1=0

⇒a=1

SIMILARLY ,

b²-2b+1=0

⇒(b-1)²=0

⇒b=1

a²+b²=1²+1² =2