xsquare-x-6 and x square+3a-18 have common factor (x-a) and find value of a
Answers
Answer:
Value of a is 3.
Step-by-step explanation:
Given that x²-x-6 and x²+3a-18 have a common factor as ( x-a ) .So , firstly on equating x-a with 0 , we get ;
=>x-a=0
=>x=0+a.
=>x=a .
Hence x=a is a zero of both quadratic polynomials.
Put x=a in x²-x-6 :-
=>p(x) = x²-x-6.
=>p(a) = a²-a-6 = 0.
=>a²-a-6 = 0 .
=>a²-3a+2a-6 = 0.
=>a(a-3)+2(a-3) = 0.
=>( a-3 )( a+2 ) = 0.
=> a = 3,(-2) ..................(i)
Put x=a in x²+3a-18 :-
=>p(x,a) = x²+3a-18.
=>p(a) = a²+3a-18 = 0.
=>a²+3a-18 = 0.
=>a²+6a-3a-18 = 0.
=>a(a+6)-3(a+6)=0.
=>( a-3 )( a+6 ) = 0.
=>a = 3,(-6)..................(ii)
From (i) and (ii) , a = 3 is common solution to both equations .
Hence the value of a is 3 .
Answer:
3
Step-by-step explanation:
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