39. For what values of a is the inequality az2 2ax + 0.5>0valid throug

1.	39. For what values of a is the inequality az2 2ax + 0.5>0valid throughout the entire number axis?
Answer» for the quadratic expression ax²+2ax+1/2 to be always positive , it's graph should have cut on x-axis , or is should not have any real roots for that D < 0=> b²-4ac <0=>(2a)²-4*(a)(1/2) <0=> 4a²-2a < 0=> 2a(2a-1) <0so, the value of. a lies between (0,1/2)

39. For what values of a is the inequality az2 2ax + 0.5>0valid throughout the entire number axis?

Answer»

for the quadratic expression ax²+2ax+1/2 to be always positive ,

it's graph should have cut on x-axis , or is should not have any real roots

for that

D < 0=> b²-4ac <0=>(2a)²-4*(a)(1/2) <0=> 4a²-2a < 0=> 2a(2a-1) <0so, the value of. a lies between (0,1/2)