Question

What is the value of \( m \) which satisfies \( 3m^2 - 21m + 30<0 \)?

• A. \( m<2 \ \text{or} \ m>5 \)
• B. \( m>2 \)
• C. \( 2<m<5 \)
• D. Both a and c

Hint:

For quadratic inequalities, factorize and use the sign chart method to determine the intervals where the expression is positive or negative.

Answer 1

The Correct Option is C

We have: \[ 3m^2 - 21m + 30<0 \] Divide throughout by 3: \[ m^2 - 7m + 10<0 \] Factorize: \[ (m - 5)(m - 2)<0 \] This quadratic inequality is negative between its roots, hence: \[ 2<m<5 \] Therefore, the range of \( m \) is \( 2<m<5 \).