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Sagot :
Answer:
first option
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
then the nature of the roots can be found using the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 , then the 2 roots are real and irrational
• If b² - 4ac > 0, and a perfect square, then 2 roots are real and rational
• If b² - 4ac = 0 , then 2 roots are real and equal
• If b² - 4ac < 0 , then 2 roots are not real
3x² + 4x - 2 = 0 ← is in standard form
with a = 3, b = 4 and c = - 2 , then
b² - 4ac = 4² - (4 × 3 × - 2) = 16 - (- 24) = 16 + 24 = 40
since b² - 4ac > 0 , then 2 real and irrational roots
Answer:
2. d = 40; 2 rational
Step-by-step explanation:
The discriminant (d) of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] is:
[tex]\boxed{\mathrm{d =} \ b^2 - 4ac}[/tex].
If:
• d > 0, then there are two real solutions
• d = 0, then there is a repeated real solution
• d < 0, then there is no real solution.
In this question, we are given the quadratic equation [tex]3x^2 + 4x - 2 = 0[/tex]. Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)
= 16 - (-24)
= 40
Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.
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