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

Answer: The answer is (c) real and irrational root .

Step-by-step explanation: The given quadratic equation is

`y^2-5y-3=0.`

We know that the discriminant of the quadratic equation
`ax^2+bx+c=0~(a\\eq 0)` is given by

`D=b^2-4ac.`

In our given equation, we have

a = 1, b= -5 and c = -3.

Therefore, the discriminant is given by

`D=b^2-4ac=(-5)^2-4* 1* (-3)=25+12=37>0.`

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).

Answer 2

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.