7. Y = 4X2 – 6X +7 A. TWO RATIONAL REAL SOLUTIONS
B. TWO IRRATIONAL REAL SOLUTIONS
C. TWO IMAGINARY SOLUTION
D. ONE REAL SOLUTION

C

Step-by-step 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