Question

Using the discriminate determine the number and type of solutions for this equation

2x^2+5x+3=0

Answer 1

two complex conjugate numbers

Explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the discriminant

Δ = b² - 4ac , informs us about the nature of the solutions

• if b² - 4ac > 0 , then two real, irrational solutions

• if b² - 4ac > 0 and a perfect square, then two real, rational solutions

• if b² - 4ac = 0 , then one real, rational solution (double)

• if b² - 4ac < 0 , then two complex conjugate solutions

given

4x² - 7x + 4 = 0 ← in standard form

with a = 4, b = - 7 , c = 4 , then

b² - 4ac

= (- 7)² - (4 × 4 × 4)

= 49 - 64

= - 15

since b² - 4ac < 0 , then two complex conjugate solutions