Question

if a-b, a+b are the zeros of x^2-4x+3 then (a, b) =


A) (3, 1)
B) (-3,-1)
C) (2, 1)
D) (-2,-1)​

Answer 1

Answer:-

(Let a = α & b = β).

Given:

α - β , α + β are the zeroes of x² - 4x + 3.

On comparing with standard form of a quadratic equation i.e., ax² + bx + c = 0 ;

Let ;

• a = 1
• b = - 4
• c = 3.

We know that,Sum of the zeroes = - b/a

⟹ α - β + α + β = - ( - 4)/1

⟹ 2α = 4

⟹ α = 4/2

⟹ α = 2

And,

Product of the zeroes = c/a

⟹ (α - β) * (α + β) = 3/1

• (a + b) * (a - b) = a² - b².

⟹ α² - β² = 3

Putting the value of α we get,

⟹ (2)² - β² = 3

⟹ 4 - 3 = β²

⟹ 1 = β²

⟹ √1 = β

⟹ 1 = β

∴(a , b) = (α , β) = (2 , 1). (Option - C).