Question

Two roots of $4x^3+8x^2+Kx-18=0$ are equal numerically but opposite in sign. Find the value of K.

• A. $-2$
• B. $+2$
• C. $-9$
• D. $+9$

Answer 1

The correct option is C $-9$

• Let the two roots be $a$ and $-a$ , let the other root be $b$
• We have $a-a+b=-8/4=-2$ , which implies $b=-2$
• We have $a\times -a\times b=18/4=9/2$ , which implies $a^2=9/4$
• Therefore we get $a=3/2$
• We get $K/4=ab-ab-a^2=-a^2=-9/4$ , Therefore we get $K=-9$