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JEE Main 20208 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
8 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2020 · 8 January · Morning Shift · Mathematics · Quadratic Equation

The least positive value of ‘ a ’ for which the...

The least positive value of ‘ aa ’ for which the equation, 2x2+(a−10)x+332=2a2{x}^{2} + \left(a - 10\right)x + \dfrac{33}{2} = 2a has real roots is ___________.

Correct answer

0

Step-by-step solution

D≥0D \ge 0
(a−10)2−4(2)(332−2a)≥0{\left(a - 10\right)}^{2} - 4\left(2\right)\left(\dfrac{33}{2} - 2a\right) \ge 0
(a−10)2−4(33−4a)≥0{\left(a - 10\right)}^{2} - 4\left(33 - 4a\right) \ge 0
a2−4a−32≥0⇒a∈(−∞,−4)∪[8,∞){a}^{2} - 4a - 32 \ge 0 ⇒ a \in \left(- \infty, - 4\right) \cup \left[8, \infty\right)
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