CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
The quadratic equation 4x^2 - 12x + 9 = 0 has roots that are:
The discriminant is 144 minus 144, which is zero. So the roots are real and equal, both being 3/2, which is rational. The equation is the perfect square of (2x - 3).
- Areal, equal and rationalCorrect
- Breal, unequal and irrational
- Creal, unequal and rational
- Dimaginary
Explanation
D = (-12)^2 - 4(4)(9) = 144 - 144 = 0. A zero discriminant gives real and equal roots, each equal to 12/8 = 3/2, which is rational. The equation is (2x - 3)^2 = 0.
Did you get it right without looking?
One question tells you little. A timed set on Quadratic Equations shows your real accuracy, how long you take and where you lose marks.
More Quadratic Equations questions
- The roots of the equation x^2 - 7x + 12 = 0 are:
- For the quadratic equation 3x² − 12x + k = 0 to have two equal real roots, what must be the value of k?
- For the equation 2x^2 - 8x + k = 0, the roots are real and equal. What is the value of k?
- If α and β are the roots of 3x² − 6x + 2 = 0, what is the value of α² + β²?
- The sum of the roots of 2x^2 - 11x + 14 = 0 is S and the larger root is L. What is the value of S + L?
- For which range of values of m does the equation x² + mx + 9 = 0 have no real roots?