Web Analytics
Answered



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

Verified Answer :

sqdancefan

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

\(y^2-5y-3=0.\)

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

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

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).

Related Questions