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

Answer 1

(C) 2x² – 7x + 6 = 0

Step-by-step explanation:

There are two methods to solve it..

1st. finding the roots of all option (quite long)

2nd. Putting the value of 2 as a root in all option

I will follow the 2nd one

So,

$(A) {x}^{2} - 4x + 5 \\ \\ = ( {2)}^{2} - 4.2 + 5 \\ \\ = 4 - 8 + 5 \\ \\ = 9 - 8 \\ \\ = 1 \\ \\ (B){x}^{2} + 3x - 12 \\ \\ = {(2)}^{2} + 3.2 - 12 \\ \\ = 4 + 6 - 12 \\ \\ = 10 - 12 \\ \\ = - 2 \\ \\(C) 2 {x}^{2} - 7x + 6 \\ \\ = 2( {2)}^{2} - 7.2 + 6 \\ \\ = 2.4 - 14 + 6 \\ \\ = 8 - 8 \\ \\ = 0$

We don't need to solve last one because we get the answer.

So, the answer is Option C

Answer 2

$\rule{200}4$

$\huge\tt{GIVEN:}$

• Equations in which we have to find whose root is 2 ?

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$\huge\tt{CONCEPT~USED:}$

• We can either find the root to all of them which is very time consuming or We can simply put the value of 2 as a root in the place of x in the given options

$\rule{200}3$

$\huge\tt{SOLUTION:}$

Let's start with doing it to option (A)

(A) x² – 4x + 5 = 0

⇝(2)² - 4.2 + 5

⇝4 - 8 + 5

⇝9 - 8

⇝1

Clearly, This is not the required answer as it have 1 as root.

$\rule{200}2$

Now, Let's see if option (B) is having 2 as it's root

(B) x² + 3x – 12 = 0

⇝(2)² + 3.2 - 12

⇝4 + 6 - 12

⇝10 - 12

⇝ -2

This option is also not having 2 as it's root, so it is not the required answer

$\rule{200}2$

Now, Let's see if option (C) is having 2 as it's root

(C) 2x² – 7x + 6 = 0

⇝2(2)² - 7.2 + 6

⇝2.4 - 14 + 6

⇝ 8 - 8

⇝0

We can see that option (C) is having the correct root as the Answer is 0 , which means it's root is 2 , So we got our answer i.e., 2x² – 7x + 6 = 0 .

$\rule{200}5$