the root of the equation 2x²+ a x -a² equal to zero is
Share
the root of the equation 2x²+ a x -a² equal to zero is
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Step-by-step explanation:
Quadratic equations 3x
2
+ax+1=0 and 2x
2
+bx+1=0 have a common root.
Let α be the common root.
⇒3α
2
+aα+1=0…(1)
and 2α
2
+bα+1=0…(2)
Multiplying (1) by 2 and (2) by 3.
Further solving those two equations for α gives
α=b−a…(3)
Substituting (3) in(1)
⇒2(b−a)
2
+b(b−a)+1=0
⇒3b
2
+2a
2
−5ab+1=0
∴5ab−3b
2
−2a
2
=1