If $a, b, c, d$ be a form consecutive term of an increasing A.P., then the roots of the equation $\left( {x - a} \right)\left( {x - c} \right) + 2\left( {x - b} \right)\left( {x - d} \right) = 0$

$\begin{array}{l} (x-a)(x-c)+2(x-b)(x-d)=0 \quad[d>c>b>d] \\ f(a)=0+2(a-b)(a-d)>0 \\ f(b)=(b-a)(b-c)+2 \times 0<0 \\ f(c)=0+2(c-b)(c-d)<0 \\ f(d)=(d-a)(d-c)+2 \times 0>0 \end{array}$

$x \in$ Real and distinct