Question

Use the discriminant to determine the nature of the roots of the following equation.

y2 - 5y - 3 = 0

Double root
real and rational root
real and irrational root
non-real root

Answer 1

The standard form of a quadratic equation is ,

ax² + bx + c = 0.

And the formula to find the discriminant is b² - 4ac.

First step is to compare the given equation with this equation to get the value of a, b and c.

After comparing the equations we will get a = 1, b = -5 and c = -3.

So, discriminant = b²- 4ac

=( -5)²-4 (1)(-3)

= 25 + 12

= 37

So, discriminant of the given equation is 37.

37 is greater than 0 and it's not a perfect square number.

So, square root of 57 will result real and irrational number.

Hence, third choice is correct.

Hope this helps you!