If p^2x^2 – q^2 = 0, then x =?
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10th
Maths
Quadratic Equations
Solutions of Quadratic Equations
If (p2 - q2)x2 + (q2 - r2)x...
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Asked on January 17, 2020 by
Farhaz Mohata
If (p
2
−q
2
)x
2
+(q
2
−r
2
)x+r
2
−p
2
=0 and (p
2
−q
2
)y
2
+(r
2
−p
2
)y+q
2
−r
2
=0 have a common root for all real values of p, q and r, then find the common root.
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ANSWER
(p
2
−q
2
)x
2
+(q
2
−r
2
)x+r
2
−p
2
=0 ....(1)
The sum of the coefficients (p
2
−q
2
)+(q
2
−r
2
)+(r
2
−p
2
)=0
Therefore, x=1 is a root of equation 1.
(p
2
−q
2
)y
2
+(r
2
−p
2
)y+q
2
−r
2
=0 .....(2)
p
2
−q
2
+r
2
−p
2
+q
2
−r
2
=0
Therefore, y=1 is a root of equation 2.
Therefore, 1 is the common root of equations 1 and 2.
I hope it will help you ☺️
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