Find the value of a

Question

Te equation 2x(ax-4)-x^2+6=0 has no real roots. What is the smallest possible integer value of a?

Answer 1

2x(ax-4)-x²+6=0

Rewritten:

2ax² - 8x - x² + 6 = 0

(2a - 1)*x² - 8x +6 = 0

For this polynomial to have no real roots, then:

(-8)² -4*(2a-1)*6 < 0

64 -48a +24 < 0

-48a < -88

48a > 88

a> 11/6

Therefore, the smallest possible integer value of a is 2