1. If (x - 2) and (x + 3) are the factors of the equation $$x^{2} + k_1x + k_2 = 0$$, then what are the values of $$k_1$$ and $$k_2$$ ?
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By: anil on 05 May 2019 01.48 am
Equation : $$f(x)=x^{2} + k_1x + k_2 = 0$$ If $$(x-2)$$ and $$(x+3)$$ are factors of above equation, then $$x=2,-3$$ will satisfy above equation. => $$f(2)=(2)^2+k_1(2)+k_2=0$$ => $$2k_1+k_2=-4$$ ----------(i) Similarly, $$f(-3)=(-3)^2+k_1(-3)+k_2=0$$ => $$-3k_1+k_2=-9$$ ----------(ii) Subtracting equation (ii) from (i), we get : => $$5k_1=-4+9=5$$ => $$k_1=frac{5}{5}=1$$ Substituting it in equation (i), => $$k_2=-4-2(1)=-4-2=-6$$ => Ans - (B)
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