Question

Find the discriminant of X^2+ 4x - 3 = 0

and determine the number of real
solutions of the equation.

Answer 1

2 real solutions

Explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ), then the discriminant is

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real and distinct solutions

• If b² - 4ac = 0 then 2 real and equal solutions

• If b² - 4ac < 0 then no real solutions

x² + 4x - 3 = 0 ← is in standard form

with a = 1, b = 4, c = - 3 , then

b² - 4ac = 4² - (4× 1 × - 3) = 16 - (- 12) = 16 + 12 = 28

Since b² - 4ac > 0 then the equation has 2 real and distinct solutions