If the discriminant of an equation is negative which of the following is true of the equation?
(a) It has 2 complex solutions
(b) It has 2 real solutions
(c) It has one real solution.
Answer: Option (a) It has 2 complex solutions; is true if the discriminant of an equation is negative.
Let's find the value of discriminant and nature of roots.
A discriminant of a quadratic equation is a function of the coefficients of the polynomials.
The nature of roots of a quadratic equation and the type of solution can be found by the discriminant.
The discriminant is given by D = b2 - 4 ac
- If D > 0, the equation has two real solutions.
- If D = 0, the equation has real and equal solutions.
- If D < 0, the equation has no real solutions or complex solutions.
Where a = coefficient of x2, b = coefficient of x and c = constant term.