Question

if the roots of the equation x^2+7x+m =0 are two consecutive whole numbers then find m​

Answer 1

SOLUTION

GIVEN

The roots of the equation x² + 7x + m = 0 are two consecutive whole numbers

TO DETERMINE

The value of m

EVALUATION

Here the given Quadratic equation is

x² + 7x + m = 0

Now it is given that the roots of the equation are two consecutive whole numbers

Let the roots are r and r + 1

Where r is a whole number

Then

Sum of the roots = - 7

⇒ r + r + 1 = - 7

⇒ 2r + 1 = - 7

⇒ 2r = - 8

⇒ r = - 4

So the roots are - 4 and - 3

But - 4 & - 3 are not whole numbers

So in that case m can not be determined

Let we find the value of m assuming roots as an integer

So the roots are - 4 & - 3

Thus

m = Product of the roots = - 4 × - 3 = 12

FINAL ANSWER

Hence the required value of m = 12

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