usmam.org->Polynomials-and-rational-expressions-> SOLUTION: resolve the equationx^3+4x^2-9x-6=0giving every root in specific formI perform not even know how to start this question, sorry! var visible_logon_form_ = false;Log in or register.Username: Password: register in one simple step!.Reset her password if girlfriend forgot it."; return false; } "> log On

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Click below to see ALL problems on Polynomials-and-rational-expressionsQuestion 717575: deal with the equationx^3+4x^2-9x-6=0giving each root in an exact formI carry out not also know how to begin this question, sorry! answer by jsmallt9(3758)
(Show Source): You can put this systems on your website! very first of all, shot to article your questions in an suitable category. This difficulty has naught to perform with logarithms. (I have readjusted the group to an proper one.)To fix an equation choose this we want a zero ~ above one side and also then we try to aspect the other side. Due to the fact that we already have a zero top top one next we have the right to go straight to the factoring. The greatest usual factor is 1 (which we seldom bother factoring out). With 4 terms, there space too numerous terms because that factoring v patterns or for trinomial factoring. Ns don"t see a means to variable by grouping so every we have left is factoring by trial and error the the possible rational roots.The possible rational roots of a polynomial space all the feasible ratios, positive and negative, which have the right to be created using a variable of the continuous term (at the end) end a factor of the top coefficient (at the front). The continuous term of this polynomial is 6. (Actually the is -6 but due to the fact that we"re going to incorporate all positive and an unfavorable ratios anyway, that doesn"t matter if we use 6 or -6.) The factors of 6 room 1, 2, 3 and also 6. The top coefficient is 1 whose factors are 1"s. For this reason the feasible rational roots of the left side are:+1/1, +2/1, +3/1 and +6/1which leveling to:+1, +2, +3 and also +6If a number, let"s call it "r", is a root of a polynomial climate (x-r) is a variable of the polynomial. We can inspect 1 and also -1 mentally due to the fact that powers of 1 and also -1 are simple. Neither of these numbers rotate out to be roots.For the other feasible rational root we space going to use synthetic division to watch if (x-r) (where "r" is just one of our possible rational roots) is a factor. Staring with 2:2 | 1 4 -9 -6---- 2 12 6 ----------------- 1 6 3 0The number in the lower right corner is the remainder. A zero remainder means that (x-2) separated evenly into the polynomial. This also means that (x-2) is a element of the polynomial. Not only that, the remainder of the bottom heat tells use what the other aspect is. The "1 6 3" translates into The left side is now:Neither element will factor further.

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Now we have the right to use the Zero Product Property: or resolving the very first equation is easy, x = 2. To fix the 2nd equation we must use the Quadratic Formula:Simplifying...which is brief for: or therefore there are three options to your equation: or or