Question

Which of the following equations has $2$ as a root?

(A) $x^2-4x+5=0$

(B) $x^2+3x-12=0$

(C) $2x^2-7x+6=0$

(D) $3x^2-6x-2=0$

• A. (A)
• B. (B)
• C. (C)
• D. (D)

Answer 1

The correct option is C

(C)

Explanation for the correct option:

Option (C): Consider $2x^2-7x+6=0$.

Substitute $x=2$ into the given equation to find whether the equation has $2$ as a root.

$\begin{array}{rcl}2\times 2^2-7\left(2\right)+6& =& 0\\ & \Rightarrow & 8-14+6=0\\ & \Rightarrow & 0=0\end{array}$

Hence, option (C) is correct.

Explanation for the incorrect options:

Option (A): Consider $x^2+3x-12=0$.

Substitute $x=2$ into the given equation to find whether the equation has $2$ as a root.

$\begin{array}{rcl}{2}^2+3\left(2\right)-12& =& 0\\ & \Rightarrow & 4+6-12=0\\ & \Rightarrow & -2\ne 0\end{array}$

Therefore, option (A) is incorrect.

Option (B): Consider $x^2-4x+5=0$.

Substitute $x=2$ into the given equation to find whether the equation has $2$ as a root.

$\begin{array}{rcl}{2}^2-4\left(2\right)+5& =& 0\\ & \Rightarrow & 4-8+5=0\\ & \Rightarrow & 1\ne 0\end{array}$

Therefore, option (B) is incorrect.

Option (D): Consider $3x^2-6x-2=0$.

Substitute $x=2$ into the given equation to find whether the equation has $2$ as a root.

$\begin{array}{rcl}3·2^2-6\left(2\right)-2& =& 0\\ & \Rightarrow & 12-12-2=0\\ & \Rightarrow & -2\ne 0\end{array}$

Therefore, option (D) is incorrect.

Thus, options (A), (B), and (D) are incorrect.

Hence, option (C) is correct.