Question

What are the approximate solutions of 5x2 − 7x = 1 rounded to the nearest hundredth?

No real solutions

x ≈ −0.65 and x ≈ 7.65

x ≈ −1.53 and x ≈ 0.13

x ≈ −0.13 and x ≈ 1.53

Answer 1

ok you should solve this using Quadratic equation.
\[\huge 5x^2-7x-1=0\]
here
a=5,b=-7,c=-1

Answer 2

@rebecca1233 did you get it?

Answer 3

OK, quick and dirty, without a huge amount of calculation.

The quadratic function opens upwards (leading coefficient positive) and the y-intercept is negative. That means there will be two distinct real roots, so the first answer out.

The axis of symmetry for the graph is x=-b/2a=7/10, so the solutions have to be equal distance above and below that x value. The only one of your given answers that meets that specification is the last one.

Answer 4

Think about the way the graph looks, and you can narrow the field of possible solutions quickly. Of course, you can grind it out as shown very nicely by sami-21.