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Nature of Roots

Show that the...

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Show that the equation [a-2] x^2 + [2-b]x + [b-a] = 0 has equal roots , if 2a = b+2

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Similar questions

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

x^{2} - p x + q = 0

have a root in common and the second equation has equal roots, show that

b + q = \frac{a p}{2} .

Q. Show that the equation

2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0

has no real roots, when

a \neq b

Q. If the roots of the equation

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

are equal, prove that

2 a = b + c

Q. If the roots of the quadratic equation

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

are equal, prove that

2 a = b + c

Q. If the equation

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

has two positive and real roots, then the equation

3 a x^{2} + (2 a + 3 b) x + b + 3 c = 0

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