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Nature of Roots

If the roots ...

Question

If the roots of the equations $(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0$ are equal, then

(a) 2b = a + c
(b) b² = ac
(c) $b = \frac{2 a c}{a + c}$
(d) b = ac

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Solution

The given quadric equation is , and roots are equal.

Here,

As we know that

Putting the value of

The given equation will have equal roots, if

Thus, the correct answer is

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Similar questions

Q. If the equation

(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0

has both roots equal, then
(a) b = ac
(b)

b = \frac{1}{2} (a + c)

(c) b² = ac
(d)

b = \frac{2 a c}{(a + c)}

Q. If the roots of the equation

(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0

Q. If the roots of

(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0

are real and equal then

a, b, c

a, b, c, x

are real numbers and

(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0

has real & equal roots, then

a, b, c

(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) \geq 0

x ϵ R

. If equality holds then find the ratio of the roots of the equation

a x^{2} + 2 b x + c = 0

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