Let D1=∣∣∣∣xab−10xx21∣∣∣∣ and D2=∣∣∣∣cx22a−bx21−10x∣∣∣∣. If all the roots of the equation (x2−4x−7)(x2−2x−3)=0 satisfies the equation D1+D2=0, then the value of a+4b+c is

Let D1=∣∣∣∣xab−10xx21∣∣∣∣ and D2=∣∣∣∣cx22a�

1.	Let D1=∣∣∣∣xab−10xx21∣∣∣∣ and D2=∣∣∣∣cx22a−bx21−10x∣∣∣∣. If all the roots of the equation (x2−4x−7)(x2−2x−3)=0 satisfies the equation D1+D2=0, then the value of a+4b+c is
Answer» Let $D_{1} = ∣ ∣∣ ∣ \begin{matrix} x & a & b - 1 & 0 & x x & 2 & 1 \end{matrix} ∣ ∣∣ ∣$ and $D_{2} = ∣ ∣∣ ∣ \begin{matrix} c x^{2} & 2 a & - b x & 2 & 1 - 1 & 0 & x \end{matrix} ∣ ∣∣ ∣ .$ If all the roots of the equation $(x^{2} - 4 x - 7) (x^{2} - 2 x - 3) = 0$ satisfies the equation $D_{1} + D_{2} = 0,$ then the value of $a + 4 b + c$ is