Question

If 17 times a number is subtracted from
double of its square, we get 84 as remainder.
What is the number?
(1) 10
(2) 11
(3) 12
(4) 13
(5) None of these​

Answer 1

AnswEr:

Option (3) is correct.

Step-by-step explanation:

Let the number be x.

According to the question,

2x² - 17x = 84...........(1)

Splitting middle term,

: $\implies$ 2x² - 24x + 7x - 84 = 0

: $\implies$ 2x ( x - 12 ) + 7 ( x - 12 ) = 0

: $\implies$ ( 2x + 7 ) ( x - 12 ) = 0

: $\implies$ 2x + 7 = 0 and x - 12 = 0

: $\implies$ x = - $\dfrac{7}{2}$ and x = 12

From the given options, we get, x = 12.

$\therefore$ Option (3) is correct.

$\rule{200}2$

VerificaTion:

Put x = 12 in (1),

: $\implies$ 2 ( 12 )² - 17 ( 12 ) = 84

: $\implies$ 2 ( 144 ) - 204 = 84

: $\implies$ 288 - 204 = 84

: $\implies$ 84 = 84

Verified.

Answer 2

Solution :

Let the number be x .

According to the question :

17 times a number ( 17x ) is subtracted from double of its square ( 2x² ) , we get 84 as remainder.

2x² – 17x = 84

→ 2x² – 17x – 84 = 0

By middle term splitting method

→ 2x² – (24 – 7)x – 84 = 0

→ 2x² – 24x + 7x – 84 = 0

→ 2x(x – 12) + 7(x – 12) = 0

→ (x – 12)(2x + 7) = 0

x – 12 = 0

→ x = 12

2x + 7 = 0

$\rightarrow \sf{2x = - 7} \\ \rightarrow \sf{x = - \dfrac{7}{2} }$

From the above given 5 options :

We found x = 12

So, option (3) is the correct answer .