Given:
α - β , α + β are the zeroes of x² - 4x + 3.
Find:
The coordinates of (a,b)
Solution:
(Let a = α & b = β).
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).
I hope it will help you.
Regards.
