The least positive value of ‘ a ’ for which the equation, 2 x 2 + a - 10 x + 33 2 = 2 a has real roots is ___________.

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Question: Answered & Verified by Expert

The least positive value of ‘

a

’ for which the equation,

2 x^{2} + (a - 10) x + \frac{33}{2} = 2 a

has real roots is ___________.

MathematicsQuadratic EquationJEE MainJEE Main 2020 (08 Jan Shift 1)

Solution:

1980 Upvotes Verified Answer

The correct answer is: 8

D \geq 0

{(a - 10)}^{2} - 4 (2) (\frac{33}{2} - 2 a) \geq 0

{(a - 10)}^{2} - 4 (33 - 4 a) \geq 0

a^{2} - 4 a - 32 \geq 0 \Rightarrow a \in (- \infty, - 4) \cup [8, \infty)

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