Q. 95.0( 3 Votes )

# Write the condition to be satisfied for which equations ax^{2} + 2bx + c = 0 and have equal roots.

Answer :

Given the roots of both the equations are real

For first equation ax^{2} + 2bx + c = 0

Its discriminant; d ≥ 0

D = b^{2} – 4ac

D = (2b)^{2} – 4 × a × c ≥ 0

4b^{2} ≥

b^{2} ≥ ac …1

For second equation

d = b^{2} – 4ac ≥ 0

= (2)^{2} – 4 b xb ≥ 0

= 4ac – 4 b^{2} ≥

ac ≥ b^{2} …2

From 1 and 2 we get only one case where b^{2} = ac

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