Question

What is the value of the discriminant for the quadratic equation 0 equals X squared minus 4X +5 and how many number of real solutions does the equation have

Answer 1

Answer:

Discriminant: -4

No real solutions

Step-by-step explanation:

You might remember this long, seemingly very hairy thing called the quadratic formula from earlier in algebra:

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

The discriminant of a quadratic equation of the form $ax^2+bx+c=0$ is that bit under the square root: $b^2-4ac$. What does the discriminant tell us? Since we're taking its square root, we know that $\sqrt{b^2-4ac}$ is only real for non-negative values of $b^2-4ac$. If $b^2-4ac > 0$, we have two real roots, one for $\sqrt{b^2-4ac}$ and one for $-\sqrt{b^2-4ac}$. If $b^2-4ac = 0$, the function has a rational root, since the formula becomes

$x=\frac{-b}{2a}$

In your case, we have the equation $x^2-4x+5$; here, $a=1$, $b=-4$, and $c=5$, so our discriminant is $(-4)^2-4(1)(5)=16-20=-4$. Since we'd have a negative under our square root in the quadratic formula, we have no real solutions.

Answer 2

Answer:-5

Step-by-step explanation: