Question

Which of the following statements has the truth value 'F'?

• A. A quadratic equation has always a real root
• B. The number of ways of seating $2$ persons in two chairs out of n persons is $P\left(n,2\right)$
• C. The cube roots of unity are in GP
• D. 4) None of the above

Answer 1

The correct option is A

A quadratic equation has always a real root

The explanation for the correct option:

Option A:

The nature of the roots of the quadratic equation is determined by the determinant $D$

For a quadratic equation of the form $a{x}^2+bx+c=0$, the determinant is $b^2-4ac$.

If $D>0$, the roots are real and distinct.

If $D=0,$the roots are real and equal.

If $D<0,$the roots are imaginary.

So a quadratic equation may not always have real roots.

Hence option A is correct.

Explanation for the incorrect options:

Option B: $2$persons out of $n$ number of people can be seated in ${}^{n}P_2$ ways.

Option C: The cube roots of unity are $1,\omega ,{\omega }^2$.It is GP with common ratio $\omega$.

Hence option A is correct.