Express each of the following quadratic equations as the difference of two squares and solve : 1. $\,\,x^2+1=0 \\ \Ri…

5. Solve the following quadratic equations using Sridhar Acharya's formula : $\,(i)\, 2x^2+(4i-5)x+8+i=0 \\ \,(ii…

3. Solve by factorization:  $\,(i)\, 3x^2+8ix+3=0 \\ \Rightarrow 3x^2+8ix-3i^2=0 \\ \Rightarrow 3x^2+9ix-ix-3i^2=0 \\…

1. Show that  the roots of each of the following quadratic equations are complex numbers. Find the solutions in each ca…

16. If $\,x\,$ is real, find the signs of each of each of the following expressions: $\,(i)\,3x^2-2x+1 \,\,\, (ii)\,\…

7. If $\,\alpha\,$ be a root of the equation $\,\,ax^2+bx+c=0,\,\,$ show that $\,\,k\alpha\,(k \neq 0)\,\,$ is a root …

In previous article , we have discussed  Quadratic Equation : Long Answer Type Questions (33-38) of S.N. Dey math exer…

18. Using the set operations find the H.C.F. of the numbers $\,\,12,15 \,\text{and}\, 18.$ Sol. Let $\,\,A,B,C\,\,$ d…

In previous chapter , we have discussed  Quadratic Equation : Long Answer Type Questions (33-38) of S.N. Dey math exerc…

33. If $\,x\,$ is real then find the greatest and least values of : $(i)\,\frac{x^2+14x+9}{x^2+2x+3}\,\,\,(ii) \,\frac{…

28. If $\,c\,$ is real, show that the roots of the quadratic equation $\,cx^2+(c-1)x+1-2c=0\,\,$ are real. If the sum…

In the previous article , we have discussed Long Answer Type Questions (From Qst. 16-20) of S.N. Dey Math Exercise. …

In the previous article , we have discussed Long Answer Type Questions (From Q. 8-15) of S.N. Dey Math Exercise. In…