TEZPUR 2025 — Mathematics PYQ

To find the roots of the equation, we can use the substitution method to simplify the quadratic expression.

1. Substitution:

Let $x=(a+1)$. Substituting this into the equation:

$$x^2-2x=0$$

2. Factorization:

Now, factor out the common term $x$:

$$x(x-2)=0$$

This gives us two possible values for $x$:

$$x=0\text{or}x=2$$

3. Back-substitution:

Now replace $x$ with $(a+1)$ to solve for $a$:

• Case 1: $a+1=0⟹a=-1$

• Case 2: $a+1=2⟹a=1$

4. Conclusion:

The equation has two distinct real roots, which are $a=-1$ and $a=1$.

The correct answer is that the equation has two real roots.