Let α = maxₓ∈ᵣ{8²sin³ˣ 4⁴cos³ˣ} and β = minₓ∈ᵣ{8²sin³ˣ 4⁴cos³ˣ}. If 8x² + bx + c = 0 is a quadratic equation whose roots are α¹/⁵ and β¹/⁵, then the value of c – b is equal to :
Let α = maxₓ∈ᵣ{8²sin³ˣ 4⁴cos³ˣ} and β = minₓ∈ᵣ{8²sin³ˣ 4⁴cos³ˣ}. If 8x² + bx + c = 0 is a quadratic equation whose roots are α¹/⁵ and β¹/⁵, then the value of c – b is equal to :
Option 1 -
42
Option 2 -
43
Option 3 -
47
Option 4 -
50
-
1 Answer
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Correct Option - 1
Detailed Solution:α=max {2? sin³?2? cos³? }
=max {2? sin³? 2? cos³? }=2¹?
β=min {2? sin³?2? cos³? }=2? ¹?
α¹/? +β¹/? = b/8
⇒4+1/4 = b/8
⇒17/4 = b/8 ⇒ b=-34
Again α¹/? β¹/? =c/8
⇒4×1/4 = c/8
⇒c=8
⇒c−b=8+34=42
Similar Questions for you
16cos2θ + 25sin2θ + 40sinθ cosθ = 1
16 + 9sin2θ + 20sin 2θ = 1
+ 20sin 2θ = 1
– 9cos 2θ + 40sin 2θ = – 39
48tan2θ + 80tanθ + 30 = 0
24tan2θ + 40tanθ + 15 = 0
-> ,
So will be rejected as
Option (4) is correct.
12x =
is the solution of above equation.
Statement 1 is true
f(0) = – 1 < 0
one root lies in , one root is which is positive. As the coefficients are real, therefore all the roots must be real.
Statement 2 is false.
tan2 A = tan B tan C
It is only possible when A = B = C at x = 1
A = 30°, B = 30°, C = 30°
a = sin−1 (sin5) = 5 − 2π
and b = cos−1 (cos5) = 2π − 5
∴ a2 + b2 = (5 − 2π)2 + (2π − 5)2
= 8π2 − 40π + 50
sin 2 + tan 2 > 0
Let tan = x
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