Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
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.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.