If the roots of the quadratic equation kx2 + (a + b)x + ab are (-1) and (-b), then the value of k is?
An equation of the form ax2 + bx + c = 0, where a ≠ 0 is called a quadratic equation.
Answer: The value of k is 1, if the roots of the quadratic equation kx2 + (a + b)x + ab are (-1) and (-b).
Let's find the value of k
Since '-1' and '-b' are the roots of the given quadratic equation this would mean that they would satisy the given quadratic equation.
Substituting x = -b in the quadratic equation we get,
k(-b)2 + (a + b)(-b) + ab = 0
kb2 - ab - b2 + ab = 0
kb2 - b2 = 0
b2(k - 1) = 0
Since b2 cannot be equal to 0
therefore, k - 1 = 0
k = 1
Thus, the value of k is 1.