* 1. QUADRATIC EQUATION, METHOD OF ...
Question

# * 1. QUADRATIC EQUATION, METHOD OF INTERVALS & 8 QUADRATIC EXPRESSION 1. / The difference between two roots of the equation x3 – 13x2 + 15x + 189 = 0 is 2. Then, the roots of the equation are (A) – 3, 5, 7 (B) – 3, – 7,-9 FC) 3, -5,7 VDI – 3, 7,9 If ax2 + bx + c = 0 and 2x2 + 3x + 4 = 0 have a common root where a,b,ceN (set of natural numbers), the least value of a + b + cis (A) 13 (B) 11 (C) 7 Log

JEE/Engineering Exams
Maths
Solution
145
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[ n^{3}-13 n^{2}+15 n+189=0 ] Let ( alpha beta ) - be quets [ begin{array}{l} alpha+beta+gamma=13-0 alpha beta+beta v+alpha v=15 end{array} ] ( alpha q v=-18 i ) we have fiven diffo of reots id 2 2) ( 8 cdot operatorname{ang} theta+i=h ) a) ( 0 x ) ( d) quad operatorname{can} b e ) Right Leta dhem optim a) - 3,5,7 ( alpha+beta+v=-3+5+7=9 ) which doesn't matan Loith co ( Rightarrow text { Lets Chech option d }]-3,7,9 ) Note ( alpha^{prime}+beta+gamma=-3+7+9=13 ) it matches 80 d) is comeut oppion