JAMIA 2026 — Mathematics PYQ

The correct option is (a).

Concept & Formula

For a standard quadratic equation $a{x}^2+bx+c=0$, the nature of the roots depends on the discriminant ($D$), which is given by the formula:

$$D=b^2-4ac$$

• If D > 0, the equation has two distinct real roots.

• If $D=0$, the equation has exactly one unique real root (two equal real roots).

• If D < 0, the equation has no real roots (imaginary roots).

To find which equation has only one root, we need to find the equation where $D=0$.

Step-by-Step Verification of Options

Checking Option (a): $2x^2+4x+2=0$

• Here, $a=2$, $b=4$, and $c=2$.

• Calculate the discriminant:

  $$D=(4{)}^2-4(2)(2)$$

  $$D=16-16=0$$

• Since $D=0$, this equation has only one root.

(Alternative Method for 'a': Notice that $2x^2+4x+2=0$ can be simplified by dividing by 2 to get $x^2+2x+1=0$, which is a perfect square: $(x+1{)}^2=0$. This clearly gives only one repeated root, $x=-1$.)

Checking Option (b): $2x^2+4x=2⟹2x^2+4x-2=0$

• Here, $a=2$, $b=4$, and $c=-2$.

• Calculate the discriminant:

  $$D=(4{)}^2-4(2)(-2)$$

  $$D=16+16=32$$

• Since D > 0, this equation has two distinct roots.

Checking Option (c): $x^2+4x=2⟹x^2+4x-2=0$

• Here, $a=1$, $b=4$, and $c=-2$.

• Calculate the discriminant:

  $$D=(4{)}^2-4(1)(-2)$$

  $$D=16+8=24$$

• Since D > 0, this equation has two distinct roots.

Checking Option (d): $2x^2+8x+4=0$

• Here, $a=2$, $b=8$, and $c=4$.

• Calculate the discriminant:

  $$D=(8{)}^2-4(2)(4)$$

  $$D=64-32=32$$

• Since D > 0, this equation has two distinct roots.

Conclusion

Only the equation in option (a) satisfies the condition $D=0$. Therefore, (a) is the correct answer.