Question

Form a word problem based on quadratic equation such that one of its roots

is 7.​

Answer 1

SOLUTION

TO DETERMINE

Form a word problem based on quadratic equation such that one of its roots is 7.

EVALUATION

Here we have to find a word problem based on quadratic equation such that one of its roots is 7.

Word problem :

Product of two consecutive natural number is 56 . Find the numbers

Explanation :

Let the consecutive natural numbers are n and n + 1

Then by the given condition

$\sf{n(n + 1) = 56}$

$\sf{ \implies \: {n}^{2} + n= 56}$

$\sf{ \implies \: {n}^{2} + n - 56 = 0}$

Which is required Quadratic equation one of its roots is 7

Check step :

The quadratic equation obtained is

$\sf{ {n}^{2} + n - 56 = 0}$

$\sf{ \implies \: {n}^{2} + (8 - 7)n - 56 = 0}$

$\sf{ \implies \: {n}^{2} + 8n - 7n - 56 = 0}$

$\sf{ \implies \: (n + 8)(n - 7)= 0}$

$\sf{ \implies \: n = - 8 \: , \: 7}$

Since n is a natural number

n ≠ - 8

So n = 7

Hence the required natural numbers are 7 and 8

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