OE


Let us find out roots for 2𝑥^2 − 14𝑥 + 24 = 0

We have, 2𝑥^2 − 14𝑥 + 24 = 0

Divide both sides of the equation by 2, we get 𝑥^2 − 7𝑥 + 12 = 0

𝑥^2 − 4𝑥 − 3𝑥 + 12 = 0
𝑥 (𝑥 − 4) − 3(𝑥 − 4) = 0
(𝑥 – 3)(𝑥 – 4) = 0
𝑥 = 4 or 𝑥 = 3.

So, roots for 2𝑥^2 − 14𝑥 + 24 = 0 are 4 and 3.

Let us check with the answer choices.
𝑥^2 + 1 = 0
𝑥^2 = −1

Here no real root of x exists.

B) 𝑥^2 − 2𝑥 − 3 = 0
𝑥^2 − 3𝑥 + 𝑥 − 3 = 0
We get 𝑥 = 3 and 𝑥 = −1.

Here 3 is the common root with 2𝑥^2 − 14𝑥 + 24 = 0

Since, it is a one answer question and we got that B is satisfying the equation, hence

we do not need to check the remaining answer choices.

Ans. (B)