step 1 I'm going to use the quadratic formula to solve this. And in order to do that, it has to be in s

Q^2-8 q+20=0 | Numerade

Name: Problem 42, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-06-28T01:22:29-08:00
Duration: 5 min 32 s
Channel: Meredith Moody
Description: q^2-8 q+20=0

Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable, generally written in the form ax² + bx + c = 0, where a, b, and c are constants and a is nonzero. It is a fundamental concept in algebra that represents parabolic curves when graphed on the coordinate plane.

Discriminant

The discriminant is the part of the quadratic formula, calculated as b² - 4ac, and it determines the nature of the roots of the equation. Its value indicates whether the quadratic has two distinct real roots (positive discriminant), one repeated real root (zero discriminant), or two complex conjugate roots (negative discriminant).

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), is a universal method used to solve quadratic equations. By substituting the coefficients from the equation into the formula, one can directly compute its roots, regardless of whether the quadratic is factorable by simpler methods.

Complex Numbers

Complex numbers come into play when the discriminant is negative, since taking the square root of a negative number introduces an imaginary unit, i, where i² = -1. This concept extends the real number system to solve equations that have no real solutions.

Transcript

00:01 I'm going to use the quadratic formula to solve this.

00:05 And in order to do that, it has to be in standard form.

00:08 So i'm going to subtract 20q from both sides.

00:16 And that's going to leave me with 4q squared minus 20q plus 6 equals 0.

00:27 And now that i have it in standard form, my a x squared plus bx plus c, i can identify my values.

00:33 So the a value is the coefficient of my squared term, which is 4.

00:39 My b value is the coefficient of my linear term, q, which here is negative 20.

00:47 And my c term is my constant, which here is 6.

00:51 Then i am going to write down the quadratic formula so that i have it as a reference.

00:58 X equals negative b plus or minus the square root b squared minus 4a c all over 2a i did i did sing that all right so now i'm going to substitute my values x equals negative b plus or minus the square root b squared minus 4 a c all over 2 a all right so negative times a negative is a positive plus 20 squared negative is 400 minus 4 24, 24 times 4 is 96, and 2 times 4 is 8.

02:05 So, 400 minus 96 is, what, 304? it is.

02:28 I did it in my head correctly.

02:32 Yay me.

02:34 Alright, over 8.

02:36 So now i'm going to factor 304 because i have a feeling that it's got a perfect square, at least one of them that i can factor out.

02:47 So i'm going to factor 304.

02:50 We'll do two times 152.

02:56 Do two times 76, which is two times 38, two times 19.

03:16 There we go.

03:17 There's prime.

03:18 So i have this...