How do you solve a quadratic inequality eg find the values of x for which x^2 -6x +2 < -3

First we must change our inequality so that we have a zero on one side, In this case we can add three to both sides of the inequality, this gives: x^2 - 6x +5 < 0 Now let's consider the equation y = x^2 - 6x +5 We must find the values of x for which the corresponding y value is less than zero. Let's factorise our equation in order to find our x-intercepts, the points at which y=0, we get: (x-1)(x-5)=0 meaning x=1 and x=5 are our x intercepts. As we have a positive x^2, we know our quadratic will be u shaped, so the area below the x-axis, where y is below zero and therefore x^2 - 6x +5 <0 is given by 1 < x < 5. We can confirm this by drawing our graph.

IR
Answered by Isobel R. Maths tutor

3922 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C has equation ye^(-2x) = 2x + y^2. Find dy/dx in terms of x and y.


show that f(x)=cos(x) is even and what is its graphical property


g(x) = e^(x-1) + x - 6 Show that the equation g(x) = 0 can be written as x = ln(6 - x) + 1, where x<6


((x^2+4x)/2x)-((x^2-4x)/x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences