WEBVTT
00:00:02.160 --> 00:00:11.280
If π₯ equals three is one root of the quadratic equation π₯ squared minus two ππ₯ minus six is equal to zero, find the value of π.
00:00:13.120 --> 00:00:16.520
Weβre told that π₯ equals three is a root of this quadratic equation.
00:00:17.200 --> 00:00:24.280
This means that if we substitute π₯ equals three into the quadratic expression on the left of the equation, we should get zero.
00:00:25.880 --> 00:00:34.520
Substituting the value three for π₯ gives three squared minus two π multiplied by three minus six is equal to zero.
00:00:34.520 --> 00:00:37.760
And this is an equation that we can solve in order to find the value of π.
00:00:39.320 --> 00:00:43.600
Three squared is nine, and two π multiplied by three is six π.
00:00:43.600 --> 00:00:47.120
So we have nine minus six π minus six is equal to zero.
00:00:48.760 --> 00:00:54.520
Nine minus six is equal to three, so the equation simplifies to three minus six π is equal to zero.
00:00:56.080 --> 00:01:08.600
Now to solve this equation, weβll begin by adding six π to each side of the equation as, at the moment, the coefficient or number of πs that we have is negative and itβs easier to work with a positive number of πs.
00:01:08.600 --> 00:01:12.200
Adding six π to each side gives three is equal to six π.
00:01:13.800 --> 00:01:20.160
To find the value of π, we need to divide both sides of the equation by six, giving three over six is equal to π.
00:01:21.760 --> 00:01:28.200
Now the fraction three over six can and should be simplified because both the numerator and denominator can be divided by three.
00:01:29.680 --> 00:01:33.760
Dividing three by three gives one, and dividing six by three gives two.
00:01:33.760 --> 00:01:35.720
So the value of π is one-half.