factorize x²-a²-2a+b²-c²
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(i). Given Quadratic Equation,
x² - 2ax + a² - b² - c² = 0
a , b , c ∈ R
To prove: Roots of the Equation are always real.
If the standard Quadratic Equation, Ax² + Bx + C = 0
Then Discriminant is given by, D = B² - 4AC
From given Equation,
A = 1 , B = -2a , C = a² - b² - c²
D = (-2a)² - 4(1)(a² - b² - c²) = 4a² - 4a² + b² + c²
= b² + c²
Since D > 0
⇒ Roots are Real and Distinct.
Hence Proved.Step-by-step explanation:
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