Question

If $(x+1)(x+2)(x+3)(x+4)=24$, then which of the following is true?

• A. Zero is one of the roots of the equation
• B. The given equation has no roots
• C. The given equation has exactly $24$ roots
• D. The given equation is an identity

Answer 1

The correct option is A Zero is one of the roots of the equation

$(x+1)(x+4)(x+2)(x+3)=24$
or $(x^2+5x+4)(x^2+5x+6)=24$
When multiplied, the constant term 24 will be cancelled and x will become a common factor and, hence, $x=0$ will be one of the roots.