The coefficients are a=1, b=-5, c=-3, so the discriminant b²-4ac is
... (-5)²-4(1)(-3) = 25+12 = 37
The discriminant is positive, but not a square. The two distinct roots are each real and irrational.
Answer: The answer is (c) real and irrational root .
Step-by-step explanation: The given quadratic equation is
[tex]y^2-5y-3=0.[/tex]
We know that the discriminant of the quadratic equation [tex]ax^2+bx+c=0~(a\neq 0)[/tex] is given by
[tex]D=b^2-4ac.[/tex]
In our given equation, we have
a = 1, b= -5 and c = -3.
Therefore, the discriminant is given by
[tex]D=b^2-4ac=(-5)^2-4\times 1\times (-3)=25+12=37>0.[/tex]
Since the discriminant is greater than 0 and not a perfect square, so the roots will be real but irrational.
Thus, the correct option is (c).
