Quantitative Aptitude – Algebra – Quadratic Equations – If a and b are integers such that 2x^2

Slot -2 – Quantitative Aptitude – Algebra – Quadratic Equations – If a and b are integers such that 2x^2

If a and b are integers such that 2x^2 −ax + 2 > 0 and x^2 −bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a−6b is?

Answer: 36

Solution: Given,
2x^2 −ax + 2 > 0
2{ (x-a/4)^2 – a^2/16+1} > 0 ∀ x ∈R
-a^2/16+1 > 0
a ∈{ -3,-2,-1,0,1,2,3}
x^2 −bx + 8 ≥ 0
(x-b/2)^2 – b^2 /4 + 8>0 ∀ x ∈R -b^2 /4 + 8>0
b ∈{-5,-4,-3,-2,-1,0,1,2,3,4,5 }
So largest possible value of 2a – 6b = 3*2 – 6(-5) = 36

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