NTA Abhyas JEE Main2020MathematicsSequences and SeriesPractice

If a , b , c are in arithmetic progression and one root of the equation a x 2 + b x + c = 0 is 2, then the other root is

Options

A3 4
B- 3 4
C- 5 4
D- 5 2

Correct answer

C. - 5 4

Step-by-step solution

Let α be the other root, given that 2 is a root. So, a ⋅ 2 2 + b ⋅ 2 + c = 0 ⇒ 4 a + 2 b + c = 0 Also, a , b , c are in A.P. So, 2 b = a + c ⇒ 4 a + a + c + c = 0 ⇒ 5 a = - 2 c ⇒ c a = - 5 2 = 2 × α ⇒ α = - 5 4 .

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