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Is it possible for a quadratic equation to have only one $ x $ -intercept? Explain.

Yes

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

01:15

Is it possible for the gra…

01:59

Is it possible for a line…

01:19

Can the graph of a polynom…

02:17

Is it possible for a quadr…

00:37

00:52

01:58

Can the graph of a Gaussi…

00:42

Can a graph of a rational …

00:20

03:37

Can a quadratic expression…

01:40

Is it possible for the sol…

03:38

Can a quadratic equation w…

02:33

01:14

Show that all polynomial f…

01:07

00:46

It is possible for a quadr…

00:59

If an equation has two ter…

01:27

Does every quadratic equat…

for this question. We like to know if it's possible for a quadratic equation. So something like this and we want the ex queer term to be president. So we require the is non zero. Is it possible for a function like this toe have on ly one x intercept? And the answer is yes. And for example, here we can just consider one example Let's say f of X equals X squared to find the ex intercepts. As usual, you go ahead and just send f of X equals zero. So when we do that, we have X squared equals zero and then taking the square root of B side to solve for X, you have closer minus route zero. But that's just plus or minus zero in either one of those zero. So this is an example of a function that has only one exit herself. So the answer here would be, yes, but we could go ahead and provide a little more detail here. So in general, you know that the ex intercepts, which we would get by setting f of X equals zero. So now we're going back to the general case where this is R. f we have to set this quadratic equals zero. Use the contract IQ formula. So go ahead and solve that for ex negative B plus or minus square B squared minus four A. C allover too, eh? Now we want to find values of A, B and C where, regardless of whether you use the plus for the minus sign, you only get one answer. Well, if we wanna have only one answer, we should go ahead and make this radical equal to zero. So we'LL have one X intercept only if they think the radicals zero so it is possible to have only one x intercept. And if you like to know when you will have only one X intercept, that's precisely when b squared minus four A c equals zero and that's our final answer.

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