145k views
1 vote
What is the solution set for x2+6x−16=0 ?

1 Answer

3 votes

Answer:

2, -8

Explanation:

The solution set for an equation is all of the values that make the equation true.

Factoring

One way to solve many quadratic equations, especially those with a leading coefficient of 1, is factoring. Remember that quadratic functions are written in the form of ax² + bx + c. This means that the b-value is 6 and the c-value is -16.

In order to factor the equation above, we need to find 2 factors that add to b and multiply to c. In this case, these 2 factors are -2 and 8. Now, plug these values into the form (x+A) * (x+B) = 0.

  • (x-2)(x+8) = 0

Now it is easy to see that if x = 2, then the equation will be true.

  • (2-2)(2+8) = 0
  • 0 * -6 = 0

Additionally, if x = -8, then the equation will be true. The factored form of the quadratic lets us easily see that the solution set is 2 and -8.

Solution Sets

The solution set to an equation is the values that make the equation true. Since this equation is a quadratic set equal to zero, the solution set is also the zeros of the function. Zeros are points where the function crosses the x-axis (aka where y = 0). For quadratics, there can be 0, 1, or 2 real solutions. In this case, the function crosses the x-axis in 2 separate locations, so the solution set has 2 answers.

User Omar Ali
by
8.5k points

Related questions

2 answers
1 vote
180k views
1 answer
1 vote
196k views
2 answers
0 votes
117k views