Question

the product of two positive consecutive integers is 306 we need to find the integer by B2 -4ac​

Answer 1

Positive consecutive integers are ; 17 and 18.

Step-by-step explanation:

Given :

Product of two consecutive integers = 306.

To find :

The integers.

Solution :

Let the two consecutive integers be

x and (x + 1) .

By given condition, x × (x + 1 ) = 306

=>

${x}^{2} + x = 306 \\ \implies \: {x}^{2} + x - 306 = 0$

For a quadratic equation,

$a {x}^{2} + bx + c = 0$

$x = \frac{ - b \: + - \sqrt{ {d} } }{2a}$

where,

$d \: = {b}^{2} - 4ac$

For the equation,

${x}^{2} + x - 306 = 0$

a = 1, b = 1 and c = -360.

${b}^{2} - 4ac = {1}^{2} - 4 \times 1 \times - 306 \\ \implies \: 1 + 1224 = 1225$

therefore,

$\sqrt{d} = \sqrt{1225} = 35$

Now,

$x = \frac{ - b \: + - \sqrt{ {d} } }{2a} \implies x = \frac{ - 1 \: + - 35 }{2 \times 1}$

$x \: = \frac{ - 1 + 35}{2} \: \: or \: \: \frac{ - 1 - 35}{2} \\ \implies \: x = 17 \: \: or \: \: x = - 18$

Hence, positive consecutive integers are ;

17 and 18.