Question

After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is

• A. $\dfrac{1}{3}$
• B. 2
• C. $-\dfrac{2}{9}$
• D. $\dfrac{7}{3}$

Hint:

When roots are shifted by a value $h$, use substitution $x = y + h$ and apply transformation to simplify equations.

Answer 1

The Correct Option is C

Let roots be $r_1, r_2, r_3$. Let $x = y + h$ to diminish roots. Substitute and expand in terms of $y$, equate coefficient of $y$ to zero to eliminate x-term. Solve resulting cubic in $h$ and find the product of roots (values of $h$). Product of roots in cubic is $-\dfrac{d}{a}$.