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

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: