Answers>Maths>IB>Article

Let f(x)=x^2-ax+a-1 and g(x)=x-5. The graphs of f and g intersect at one distinct point. Find the possible values of a.

If the two graphs intersect, it means that they will share the same y and x coordinates at one particular point. (I will draw diagram to show point).

Therefore, you can set f(x)=g(x) so that x^2 -ax +a -1 = x-5 Then, x^2 -x(a+1) +a + 4 = 0

If they only intersect at one particular point, this means that the previous quadratic equation has only one solution. This is translated into an equation in terms of the determinant so that the determinant must be 0.

(If necessary, I will explain the difference number of solutions that one gets for different determinants).

Then, one requires b^2 - 4ac = 0 , where b is the coefficient multiplying the x, a is the coefficient multiplying the x^2 and c is the coefficient with no x in the previous equation.

This leads to (a+1)^2-4(a+4)=0 which is a quadratic equation in a:

a^2 -2a -15 =0 , which, using the quadratic formula, has solutions a= 5 and a=-3.

AO
Answered by Andres O. Maths tutor

7688 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

The quadratic equation x^2 - 2kx + (k - 1) = 0 has roots α and β such that α^2 + β^2 = 4. Without solving the equation, find the possible values of the real number k.


What is proof by induction and how do I employ it?


When do you use 'n choose k' and where does the formula come from?


How does Euclid's algorithm give solutions to equations?


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning