Question

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?

The discriminant is −4, so the equation has 2 real solutions.
The discriminant is −4, so the equation has no real solutions.
The discriminant is 35, so the equation has 2 real solutions.
The discriminant is 35, so the equation has no real solutions.

Answer 1

The value of the discriminant in this equation is (-4)^2-4*1*5 which is -4

Just for reference;
If the value of the discriminant is negative, the equation has no real solution
If the value of the discriminant is positive, the equation has two real solutions
If the value of the discriminant is zero, the equation has one real solution.


Therefore, the discriminant is -4, so the equation has no real solutions

Answer 2

The correct option is B because the discriminant is $-4$, so the equation has no real solutions.

Given:

The equation is:

$0=x^2-4x+5$

To find:

The discriminant of the given equation.

Explanation:

In a quadratic equation $ax^2+bx+c=0$, the discriminant is:

$D=b^2-4ac$

If $D>0$, then the equation has 2 real solutions.

If $D=0$, then the equation has 1 real solution.

If $D<0$, then the equation has no real solutions.

In the given equation, we have $a=1,b=-4,c=5$.

$D=(-4)^2-4(1)(5)$

$D=16-20$

$D=-4$

Since $D<0$, therefore the equation has no real solutions.

Hence, the correct option is B.

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