The lines y=mᵢx+1/mᵢ (i=1,2,3) have slopes equal to the roots of 2m³-3m²-3m+2=0. Match each result to its value. List I List II (A) Algebraic sum of x-intercepts (P) (4√2+9√5)/4 (B) Algebraic sum of y

Question

The lines y=mᵢx+1/mᵢ (i=1,2,3) have slopes equal to the roots of 2m³-3m²-3m+2=0. Match each result to its value.

List I	List II
(A) Algebraic sum of x-intercepts	(P) (4√2+9√5)/4
(B) Algebraic sum of y-intercepts	(Q) 3/2
(C) Sum of perpendicular distances from the origin	(R) -21/4
(D) Sum of segment lengths between the coordinate axes	(S) (5√2+9√5)/10

TestHub · Accepted Answer

The slopes are − 1 , 1/2 , 2 . The x -intercepts are − 1/ m i 2 ​ , summing to − 21/4 , and the y -intercepts 1/ m i ​ sum to 3/2 . The distances are 1/ ( ∣ m i ​ ∣ 1 + m i 2 ​ ​ ) , which sum to ( 5 2 ​ + 9 5 ​ ) /10 . Segment lengths are m i − 4 ​ + m i − 2 ​ ​ , summing to ( 4 2 ​ + 9 5 ​ ) /4 .

Mathematics - Straight Lines Question with Solution | TestHub

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