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

D ≥ 0 a - 10 2 - 4 2 33 2 - 2 a ≥ 0 a - 10 2 - 4 33 - 4 a ≥ 0 a 2 - 4 a - 32 ≥ 0 ⇒ a ∈ - ∞ , - 4 ∪ 8 , ∞

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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsMedium2 minPYQ_2020

MathematicsMediumnumerical

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 ___________.

Answer:

8.00

Solution:

$D \geq 0$
${(a - 10)}^{2} - 4 (2) (\frac{33}{2} - 2 a) \geq 0$
${(a - 10)}^{2} - 4 (33 - 4 a) \geq 0$
$a^{2} - 4 a - 32 \geq 0 \Rightarrow a \in (- \infty, - 4) \cup [8, \infty)$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: PYQ_2020

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