Question

HELP PLS! THANK YOU SO MUCH! Consider the quadratic equation 3x^2-6=2x. (a) What is the value of the discriminant? (b) What does the discriminant of the quadratic equation tell about the solutions to 3x^2-6=2x

Answer 1

see explanation

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 roots.

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

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

• If b² - 4ac < 0 then roots are not real

Given

3x² - 6 = 2x ( subtract 2x from both sides )

3x² - 2x - 6 = 0 ← in standard form

with a = 3, b = - 2, c = - 6 , thus

b² - 4ac = (- 2)² - ( 4 × 3 × - 6) = 4 - (- 72) = 4 + 72 = 76

Since b² - 4ac > 0 then the solution is 2 real and distinct roots