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For which of the following values of c will there be 2 distinct real solutions to the equation 5x2 + 16x + c = 0?
- a)3
- b)12
- c)14
- d)15
- e)20
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
For which of the following values of c will there be 2 distinct real s...
The best way to solve this problem is to plug in the answer choices for c, and factor the equation, starting with answer choice F: 5x2 + 16x + 3 = 0
(5x + 1)(x + 3) = 0
5x + 1 = 0, x = -1/5
x + 3 = 0; x = −3
Answer choice A gives you 2 distinct solutions for x, so you do not need to try the remaining answer choices. Using the quadratic formula to solve the other choices will not give you real solutions.
(5x + 1)(x + 3) = 0
5x + 1 = 0, x = -1/5
x + 3 = 0; x = −3
Answer choice A gives you 2 distinct solutions for x, so you do not need to try the remaining answer choices. Using the quadratic formula to solve the other choices will not give you real solutions.
Community Answer
For which of the following values of c will there be 2 distinct real s...
Solution:
To find the values of c for which the quadratic equation 5x^2 + 16x + c = 0 has 2 distinct real solutions, we can use the discriminant formula. The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.
If the discriminant is positive (D > 0), then the quadratic equation has 2 distinct real solutions. If the discriminant is zero (D = 0), then the equation has 2 identical real solutions. And if the discriminant is negative (D < 0),="" then="" the="" equation="" has="" no="" real="" />
In this case, we have the quadratic equation 5x^2 + 16x + c = 0. Comparing this with the general form ax^2 + bx + c = 0, we can see that a = 5, b = 16, and c = c.
Now, we can calculate the discriminant D using the formula D = b^2 - 4ac. Substituting the values, we get:
D = 16^2 - 4(5)(c)
D = 256 - 20c
D = 20(16 - c)
Since we want the equation to have 2 distinct real solutions, the discriminant D must be greater than zero:
D > 0
20(16 - c) > 0
16 - c > 0
c < />
Therefore, the values of c for which the equation has 2 distinct real solutions are all values less than 16. Among the given options, the only value less than 16 is 3. Hence, the correct answer is option A: 3.
To find the values of c for which the quadratic equation 5x^2 + 16x + c = 0 has 2 distinct real solutions, we can use the discriminant formula. The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.
If the discriminant is positive (D > 0), then the quadratic equation has 2 distinct real solutions. If the discriminant is zero (D = 0), then the equation has 2 identical real solutions. And if the discriminant is negative (D < 0),="" then="" the="" equation="" has="" no="" real="" />
In this case, we have the quadratic equation 5x^2 + 16x + c = 0. Comparing this with the general form ax^2 + bx + c = 0, we can see that a = 5, b = 16, and c = c.
Now, we can calculate the discriminant D using the formula D = b^2 - 4ac. Substituting the values, we get:
D = 16^2 - 4(5)(c)
D = 256 - 20c
D = 20(16 - c)
Since we want the equation to have 2 distinct real solutions, the discriminant D must be greater than zero:
D > 0
20(16 - c) > 0
16 - c > 0
c < />
Therefore, the values of c for which the equation has 2 distinct real solutions are all values less than 16. Among the given options, the only value less than 16 is 3. Hence, the correct answer is option A: 3.
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