Question

Study the statements carefully.
Statement I: Both the roots of the equation $x^2-x+1=0$ are real.
Statement II: The roots of the equation $a{x}^2+bx+c=0$ are real if and only if $b^2-4ac\ge 0$.
Which of the following options hold?

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true and Statement II is false
• D. Statement I is false and Statement II is true

Answer 1

The correct option is D Statement I is false and Statement II is true

As we know condition for the roots to be real is $b^2-4ac\ge 0$

so as doing for the statement 1 we are getting $(-1{)}^2-4\ast 1\ast 1=(-3)$ which is less than $0$ so the roots will be unequal so statement 1 is false and statement 2 gives the right condition so its true.

Hence option d is correct.