Question

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 ​

Answer 1

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