Which of the following quadratic equations has real roots?

A quadratic equation ax
2
+bx+c=0 has real roots if its discriminant (D) is greater than or equal to zero (D≥0), where:

D=b
2
−4ac
Let's check the options one by one:

Option A: 4x
2
−7x+5=0

a=4,b=−7,c=5

D=(−7)
2
−4(4)(5)=49−80=−31<0 (Roots are imaginary)

Option B: 5x
2
−11x+7=0

a=5,b=−11,c=7

D=(−11)
2
−4(5)(7)=121−140=−19<0 (Roots are imaginary)

Option C: 5x
2
−11x+8=0

a=5,b=−11,c=8

D=(−11)
2
−4(5)(8)=121−160=−39<0 (Roots are imaginary)

Option D: 2x
2
−7x+5=0

a=2,b=−7,c=5

D=(−7)
2
−4(2)(5)=49−40=9>0 (Roots are real and distinct)

Therefore, the equation in option D has real roots.