Use the discriminant to determine whether each quadratic equation has two unequa

facas9

facas9

Answered question

2021-09-18

Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution (a double root), or no real solution, without solving the equation.
3x2+5x8=0

Answer & Explanation

odgovoreh

odgovoreh

Skilled2021-09-19Added 107 answers

Step 1
We know that for a standard quadratic equation ax2+bx+c=0, discriminant D of the given function is calculated as
D=b24ac...(1)
Now,
If D>0, roots will be real and distinct in nature.
If D=0, roots will be real and equal in nature.
If D<0, root will be imaginary in nature.
Step 2
We have, the given quadratic equation as
3x2+5x8=0
On comparing with standard equation given by equation (1), we get the result as
a=3, b=5 and c=−8
Therefore,
D=b24ac
D=(5)24(3)(8)
D=121
D>0
Since, D>0 thus roots will be real and distinct in nature.
Hence, for the quadratic equation 3x2+5x8=0, roots will be real and unequal in nature.
Nick Camelot

Nick Camelot

Skilled2023-05-29Added 164 answers

For the given equation 3x2+5x8=0, we have:
a=3, b=5, and c=8.
Now, we can calculate the discriminant:
Δ=524·3·(8)=25+96=121.
The discriminant Δ is positive (Δ>0), which means the quadratic equation has two unequal real solutions.
Therefore, the equation 3x2+5x8=0 has two unequal real solutions.
Eliza Beth13

Eliza Beth13

Skilled2023-05-29Added 130 answers

Solution:
Δ=b24ac
where a, b, and c are the coefficients of the quadratic equation ax2+bx+c=0.
For the given equation 3x2+5x8=0, we have a=3, b=5, and c=8. Substituting these values into the formula for the discriminant, we get:
Δ=(5)24(3)(8)
Simplifying further:
Δ=25+96
Δ=121
Now, based on the value of the discriminant, we can determine the nature of the solutions:
1. If Δ>0, then the quadratic equation has two unequal real solutions.
2. If Δ=0, then the quadratic equation has a repeated real solution (a double root).
3. If Δ<0, then the quadratic equation has no real solution.
In this case, since Δ=121>0, the quadratic equation 3x2+5x8=0 has two unequal real solutions.
Therefore, the quadratic equation 3x2+5x8=0 has two unequal real solutions.
madeleinejames20

madeleinejames20

Skilled2023-05-29Added 165 answers

Step 1:
To determine the nature of the solutions of the quadratic equation 3x2+5x8=0 without solving it, we can use the discriminant. The discriminant, denoted as Δ, is given by the formula:
Δ=b24ac
where a, b, and c are the coefficients of the quadratic equation in the form ax2+bx+c=0.
Step 2:
For the equation 3x2+5x8=0, we have a=3, b=5, and c=8. Substituting these values into the discriminant formula, we get:
Δ=(5)24(3)(8)
Simplifying further:
Δ=25+96
Δ=121
The discriminant Δ is positive and greater than zero, which means that there are two unequal real solutions for the quadratic equation 3x2+5x8=0.

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