Respuesta :
Answer: The graph of y=mx^2-5x-2 have no x-intercepts for m<-25/8
Solution:
y=mx^2-5x-2
To find x-intercepts we must equal y to zero:
y=0→mx^2-5x-2=0
This is a quadratic equation, and we can solve it using the quadratic formula:
ax^2+bx+c=0; a=m, b=-5, c=-2
x=[-b +- sqrt( b^2-4ac) ] / (2a)
x=[-(-5) +- sqrt( (-5)^2-4(m)(-2) ) ] / (2(m))
x=[5 +- sqrt(25+8m)] / (2m)
This equation doesn't have solution (no x-intercepts) if:
25+8m<0
This is an inequality. Solving for m: Subtracting 25 both sides of the inequality:
25+8m-25<0-25
8m<-25
Dividing both sides of the inequality by 8:
(8m) / 8 < (-25) / 8
m<-25/8
Answer: The graph of y=mx^2-5x-2 heve no x-intercepts for m<-25/8
