Question

If , for all x Ïµ R, then

Solution

Correct option is

– 5 < a < 2

        x2 + 2ax + 10 – 3a = + ive ∀ real values of x if dise 4a 2 – 4 (10 – 3 a) = – ive and sign of the first term i.e., 1 is + ive.

 ∴  a2 + 3a – 10 < 0

 or (a + 5) (– 5) < 0     

∴  – 5 < a < 2

SIMILAR QUESTIONS

Q1

If 1 lies between the roots of the equation 3x2 – 3 sin α x – 2 cos2 α = 0 then α lies in the interval

Q2

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Q3

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Q4

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Q5

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Q6

If the graph of the function y = 16x2 + 8(a + 5) x – 7a – 5 is strictly above the x – axis, then ‘a’ must satisfy the inequality

Q7

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Q8

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Q9

If the roots of the equation bx2 + cx + a = 0 be expression, then for all real values of x, the expression 3b2 x2 + 6bcx + 2c2 is

Q10

If x is real, the maximum value of  is: