if roots of the equation 2x^2-2cx+ab=0 be real and distinct prove that the roots of x^2-2(a+b)x+(a^2+b^2+c^2)=0 will be imaginary
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Answer:
If the roots of x
2
−2cx+ab=0 are real and unequal
then discriminant D>0
⇒(−2c)
2
−4ab>0
⇒4c
2
−4ab>0
⇒c
2
>ab
now in quadratic equation
x
2
−2(a+b)x+a
2
+b
2
+2c
2
=0
discriminant D={−2(a+b)}
2
−4(a
2
+b
2
+2c
2
)
=4(a+b)
2
−4(a
2
+b
2
+2c
2
)
=4(2ab−2c
2
)
=8(ab−c
2
) < 0
Since discriminant is negative
∴ The roots of the given equation will be imaginary=0
x2−2(a+$
Step-by-step explanation:
hope it helps
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