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The probability that the graph of `y=16x^2 +8(a +5)x-7a-5=0,` is strictly above the x-axis, If `a in [-20,0]`

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The probability that the graph of y=16x2+8(a+5)x-7a-5=0, is strictly above the x-axis, If a∈[-20,0] A. 1720 B. 1320 C. 720 D. 320 Select the correct answer from above options

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Correct Answer - B If the equation 16x2+8(a+5)x-7a-5=0 has imaginary roots, then Discriminant <0 ⇒64(a+5)2+64(71+5)<0 ⇒a2+17a+30<0⇒(a+15)(a+2)<0⇒-15<a<-2 Hence, required probability = -2 ∫ -15 dx 0 ∫ -20 dx = 13 20

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