Algebra Know-It-ALL
Part Three 505 Question 22-10 How can we use the quadratic formula to find the roots of the following equation? −x= 3 x^2 − 4 An ...
506 Review Questions and Answers Answer 23-2 First, we must get the equation into polynomial standard form. We can do that by ad ...
Part Three 507 Answer 23-4 If the roots are pure imaginary, then they are additive inverses. That is, one is the negative of the ...
508 Review Questions and Answers Because p and q are both positive, we know that the ratio q/p is positive. Its positive and neg ...
Part Three 509 In this case, the coefficient of x is imaginary. The coefficient of x^2 , as well as the stand-alone constant, ar ...
510 Review Questions and Answers Here, the coefficient of x^2 is real, the coefficient of x is complex, and the stand-alone cons ...
Part Three 511 Question 24-4 Imagine another quadratic function in which x is the independent variable and y is the depen- dent ...
512 Review Questions and Answers In this quadratic, a= 1 and b=−2. Therefore xv=−(−2) / (2 × 1) = 2/2 = 1 Plugging this in and w ...
Part Three 513 The fact that d < 0 tells us that the function has no real zeros, just as it tells us that the qua- dratic equ ...
514 Review Questions and Answers In this function, a=−3 and b= 7. Therefore xv=−7 / [2 × (−3)] =−7/(−6) = 7/6 Plugging this in a ...
Part Three 515 Armed with this information, we can sketch the graph. To fit it into a neat space, let’s use rectangular coordina ...
516 Review Questions and Answers Answer 25-2 An equation in binomial-cubed form can always be written like this when x is the va ...
Part Three 517 Question 25-5 What is the binomial-factor form of a cubic equation in the variable x? Answer 25-5 An equation in ...
518 Review Questions and Answers When we subtract the “b-constant” from both sides in each of these equations and then divide th ...
Part Three 519 Question 25-10 What is the smallest number of real roots that a single-variable cubic equation with real-number c ...
520 Review Questions and Answers Answer 26-3 Annth-degree equation in binomial-to-the-nth form can always be written like this w ...
Part Three 521 If we substitute the quantity (x− 3)^2 for the trinomial in the original equation, we get [(x− 3)^2 ]^2 = 0 which ...
522 Review Questions and Answers The real solution set is therefore X= {−b 1 /a 1 ,−b 2 /a 2 ,−b 3 /a 3 , ··· −bn/an} Question 2 ...
Part Three 523 Answer 26-10 We must do the following things, in the order shown below. The process can be tedious, but it’s ofte ...
524 Review Questions and Answers Plug the root(s) into one of the morphed original equations, and calculate the corre- sponding ...
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