NIMCET 2020 — Mathematics PYQ

Solution

1. Using the Property of Roots:

Since $n$ and $m$ are roots of $a{x}^2-2bx+c=0$, they must satisfy the equation:

2. Substituting the Values in the Expression:

The given expression is:

Substitute $a{n}^2+c=2bn$ and $a{m}^2+c=2bm$:

3. Simplifying the Fractions:

Cancel $b$ from the numerator and denominator of both terms:

4. Sum and Product of Roots:

From the equation $a{x}^2-2bx+c=0$:

• Sum of roots $(n+m)=\frac{-(-2b)}{a}=\frac{2b}{a}$

• Product of roots $(nm)=\frac{c}{a}$

5. Final Calculation:

Substitute these values into the expression for $E$:

Final Answer:

The value of the expression is: