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Oksana_A [137]
2 years ago
11

Can someone help me with these two problems and show work please !!

Mathematics
2 answers:
Dmitry [639]2 years ago
8 0

Answer:

13. Two real solutions.

14. No real solutions.

Step-by-step explanation:

<u>Given quadratic equations:</u>

13. x^2+7x+10=0

14. 4x^2-3x+4=0

{\large \textsf{Quadratic Formula: }} x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0

What is the discriminant?

The discriminant (Δ) is b² - 4ac, which is under the square root in the quadratic formula. It is used to determine the number of real solutions (roots) of a quadratic:

  • When b² - 4ac > 0, the quadratic has two real solutions.
  • When b² - 4ac = 0, the quadratic has one real solution.
  • When b² - 4ac < 0, the quadratic has no real (complex) solutions.

13. x² + 7x + 10 = 0

\implies a=\textsf{1},b=\textsf{7},c=\textsf{10}

<u>Find the discriminant value.</u>

\implies \Delta = b^2 - 4ac

\implies \Delta=(7)^2 - 4(1)(10)

\implies \Delta=49 - 40

\implies \Delta=9

As 9 > 0, this quadratic has two real solutions.

14. 4x² - 3x + 4 = 0

\implies a=\textsf{4},b=\textsf{-3},c=\textsf{4}

<u>Find the discriminant value.</u>

\implies \Delta = b^2 - 4ac

\implies \Delta = (-3)^2 - 4(4)(4)

\implies \Delta = 9 - 64

\implies \Delta = -55

As -55 < 0, this quadratic has no real solutions.

Learn more about quadratic equations here:

brainly.com/question/28063094

brainly.com/question/27638369

irina1246 [14]2 years ago
5 0
Work is attached to this post

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