Theory question 103
PolynomialsIf the quadratic equation (x + 1)(x + 2) = k(3x + 7) has equal roots, find the possible values of the constant k.
Show the model answer
Model answer
x2 + (3 − 3k)x + (2 − 7k) = 0
Equal roots: (3 − 3k)2 = 4(2 − 7k)
9k2 + 10k + 1 = 0, (9k + 1)(k + 1) = 0
k = −1 or k = −1/9
Explanation
Equal roots means b² − 4ac = 0.