Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

If , and are the positive roots of the equation x^3-p x^2+q x-7=0 such that =1 and p, q R and p 9 then:

Options

A|p+q|=24
Bp-q=-6
C⁻¹ + ⁻¹ = ⁻¹ ( 4 3 )
D⁻¹ + ⁻¹ = ⁻¹ ( 4 3 )=

Correct answer

D. ⁻¹ + ⁻¹ = ⁻¹ ( 4 3 )=

Step-by-step solution

aligned & + + =p & + + =q & =7 & =7 ( =1) aligned So, aligned & 1+7( + )=q & 1+7(p-7)=q & 7 p-48=q & p 9 aligned When, p=9 q=15p=8 q=6 (Not satisfied given condition) So, =1, =1, =7 So, (1) |p+q|=24 (2) p-q=9-15=-6 (4) aligned & ⁻¹ + ⁻¹ + ⁻¹ ( 4 3 ) & 4 + + ⁻¹ ( 7+ 4 3 1-7 4 3 ) ( x y>1) & 4 + + ⁻¹(-1)= aligned

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