Question

Prove that the roots of (x –a)(x−b)=h² are always real
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Answer 1

Answer:

Real and unequal

(x−a)(x−b)=b

2

⇒x

2

−(a+b)x+ab−b

2

=0

D=b

12

−4a

1

c

1

⇒(a+b)

2

−4×1×(ab−b

2

)=D

⇒D=a

2

+b

2

+2ab+4b

2

−4ab

D=(a−b)

2

+(2b)

2

As

D>0∴hasReal&unequalroots