Answer:
C
Explanation:
To determine the nature of the solutions use the discriminant
Given a quadratic equation in standard form
ax² + bx + c = 0 (a ≠ 0 ) then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 and a perfect square then 2 rational real solutions
• If b² - 4ac > 0 then 2 irrational real solutions
• If b² - 4ac = 0 then 2 real and equal solutions
• If b² - 4ac < 0 then 2 imaginary solutions
Given
y = 4x² - 6x + 7
with a = 4, b = - 6, c = 7
b² - 4ac
= (- 6)² - (4 × 4 × 7)
= 36 - 112
= - 76 < 0
Then there are 2 imaginary solutions