Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B....

Question

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0
Only one of the equations is set up so that the values of a, b, and c can be determined immediately. Which one is it? Solve it.

Accepted Answer

Hey, everyone here, we are asked to select one of the following equations that can be directly solved using the quadratic formula and then work out the values of X. So before we look at our equations, we need to recall that a quadratic equation is written in the format of A X squared plus BX plus C is equal to zero. So now we just need to look at our given equations and see which of them matches this formula. So we can see that it looks like only our first equation matches this formula. And our first equation is four X squared minus X minus 35 is equal to zero. So now we just need to identify our values for A B and C by comparing the formula with the equation. So looking at our value for a while is the coefficient of X squared, which in our case is four. Next, we have B which in our case is negative 23. And lastly the last value is our C value. So C is going to be negative 35. And so now we have identified our A B and C values. So we can move on to using the quadratic formula. So we can first find the discriminative using the formula D, the discrim is equal to B squared minus four A C. So doing this, we just need to plug in our values into this formula. So we have D is equal to the quantity of negative 23 squared minus four times four times negative 35. And now simplifying all of these values, we see that our discriminator is equivalent to 1089. So now we need to find the roots using the formulas where X sub one where X sub one is equivalent to negative B minus the square root of D all over two A. And then X sub to our second route will be negative B plus the square root of D all divided by two A. So once again, we just need to plug in our values for each variable. So we see our first root X sub one is going to be equivalent to negative the negative quantity of negative 23 minus the square root of 1089 all divided by two times four. And now just simplifying, we see that we have positive 23 minus the square root of 1089 which simplifies to 33 all divided by eight. And now just simplifying our values here, we see our first root is negative 5/4. And now moving on to our second route. We use our second formula here for X sub two. And so X sub two is equivalent to the negative quantity of negative 23 plus the square root of 1089 all divided by two times four. And now simplifying we have 23 plus all divided by eight. And now finally simplifying, we see our second root is just seven. So here we have found that X sub one is equal to negative 5/4 and X sub two is equal to seven. So our two values for X are just negative 5/4 and seven. So we have found our two solutions for X and now we are left with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations is set up so that the values of a, b, and c can be determined immediately. Which one is it? Solve it.

Key Concepts

Quadratic Equations

Factoring

Identifying Coefficients

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