g-x-6x-2-5ax-b-2-given-that-g-x-has-only-two-roots-and-are-x-1-and-x-2-find-the-value-of-a-and-b-Using-x-1-as-a-root-detemine-the-extend-to-which-x-2-is-a-root-occurance-as-a-root-

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Question Number 35513 by Rio Mike last updated on 19/May/18

$$g\left(x\right)=6x^2-5ax+b^2$$$$giventhatg\left(x\right)hasonlytworoots$$$$andare(x-1)and(x-2)$$$$findthevalueofaandb.Using$$$$(x-1)asarootdeteminethe$$$$extendtowhich(x-2)isaroot$$$$\left(occuranceasaroot\right).$$

Answered by Rasheed.Sindhi last updated on 19/May/18

$$g\left(x\right)=6x^2-5ax+b^2$$$$\because x-1\mathrm{is}\mathrm{factor}$$$$g\left(1\right)=6{\left(1\right)}^2-5a\left(1\right)+b^2=0$$$$b^2-5a=-6\dots \dots \dots .\mathrm{A}$$$$\because x-2\mathrm{is}\mathrm{factor}$$$$g\left(2\right)=6{\left(2\right)}^2-5a\left(2\right)+b^2=0$$$$b^2-10a=24\dots \dots \dots .\mathrm{B}$$$$\mathrm{A}-\mathrm{B}:5a=-30\Rightarrow a=-6$$$$\mathrm{A}\Rightarrow b^2-5(-6)=-6$$$$b^2=-6-30=-36$$$$b=\pm 6i$$$$$$

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