Q.8 Let a is negative real number and satisfy all three equations x2 - ax + 15 = 0, x2 - bx + 21 = 0 & x2 - (a + b)x +45 = 0, then find a, a, b

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add equation in and (1) and wisluact it from eg (3) ( left.a^{2}-a a+15+alpha^{2}-b a+21right]-left(2^{2}-1 a+bright)(45)=0 ) ( 2 alpha^{2}-(a+b) a+836-alpha^{2}+(a+b) a-45=0 ) ( x^{2}=9 ) [ begin{array}{l} x=13 80,12=-3 quad text { is } a text { is nyature } end{array} ] subsincula ( a=-3 ) in ( lg (1) ) ( (-3)^{2}-a(-3)+15=0 ) ( 3 a=-24 quad Rightarrow quad a=-8 ) Substatute ( alpha--3 ) wh la" (2) ( (-3)^{2}-b(-3)+21=0 ) [ 3 b div 30 ] ( b=-10 ) ( 80, quad x=-3, a=-8, b=-10 )

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