Problem

Find a value of $b$ such that the roots of $x^{2}…

04:17

Problem 25 Hard Difficulty

Find a value of $c$ such that the roots of $x^{2}+2 x+c=0$ are:
a. equal and rational.
b. unequal and rational.
c. unequal and irrational.
d. not real numbers.

Answer

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Algebra

Algebra 2 and Trigonometry

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 3

The Discriminant

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Video Transcript

you're in the situation. We've defunded discriminator t, which is equal to be square when its for a C. We can use to as be here, CSE and fun here as the Kocian that is a which becomes no to square miners. Four C, which is four minus e In part, a have to find d so that the food is equal and rational. That means diesel with zero, which makes at zero visited four minus for C, which becomes four z quanto for C, which then mean that C is equal to one since the musical Duvan known Part B, we have to find C such that the roots are unequal and rational, so that means thes griddle and zero, and it's a forfeit square. So the closest while you here for that zero that is four minus for zero Z. Quitting for that is a perfect square. So that means when c zero the volleys come purpose, where in part C, you have to find the volume See such that the values off the roots are unequal and irrational. Sweat Misty's quitters and zero for D two girls and zero in this one four minus for C that means that sea has to be smaller than one. So that means see belongs to any Well, you that is minus infinity to run. Um, it excludes. That means it doesn't belong to let excludes zero. So any value that is not zero on is between this range. The comes see for D. Yeah, we have to find values. He says that the rules don't exist. They're not real. For that, we can choose for this to be smaller than zero. So that means that four minus foresee si has to go down one. So the values off see would be one to infinity.

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