Question

Please help can't get this wrong

Use the value of the discriminant to determine the number and type of roots for the equation.
x^2 - 3x + 7 = 0
A.
2 real, rational roots
B.
1 real, rational root
C.
2 real, irrational roots
D.
2 complex roots

Answer 1

D

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, irrational roots

• If b² - 4ac > 0 and a perfect square then 2 real, rational roots

• If b² - 4ac = 0 then 2 equal roots

• If b² - 4ac < 0 then 2 complex roots

x² - 3x + 7 = 0 ← is in standard form

with a = 1, b = - 3, c = 7 , then

b² - 4ac = (- 3)² - ( 4 × 1 × 7) = 9 - 28 = - 19

Since b² - 4ac < 0 then the equation has 2 complex roots