Question

The product of two consecutive positive integers is 306 we need to Find the integers. Form Quadratic equation​

Answer 1

Answer:

Let,

$\mapsto \bf First\: Consecutive\: Integers =\: x$

$\mapsto \bf Second\: Consecutive\: Integers =\: x + 1$

According to the question :

$\bigstar$ The product of two consecutive positive integers is 306.

So,

$\implies \sf x(x + 1) =\: 306$

$\implies \sf x \times x + 1 =\: 306$

$\implies \sf x^2 + x =\: 306$

$\implies \bf x^2 + x - 306 =\: 0\: \: \bigg\lgroup \small \sf\bold{\pink{Required\: Quadratic\: Equation}}\bigg\rgroup$

By doing middle term break we get,

$\implies \sf x^2 + (18 - 17)x - 306 =\: 0$

$\implies \sf x^2 + 18x - 17x - 306 =\: 0$

$\implies \sf x(x + 18) - 17(x + 18) =\: 0$

$\implies \sf (x + 18)(x - 17) =\: 0$

$\implies \bf x + 18 =\: 0$

$\implies \sf\bold{\purple{x =\: - 18}}\: \: \bigg\lgroup \small \sf\bold{\pink{Integers\: can't\: be\: negetive}}\bigg\rgroup$

$\implies \bf x - 17 =\: 0$

$\implies \sf\bold{\purple{x =\: 17}}$

Hence, the required integers are :

$\small \dashrightarrow \sf\bold{\red{First\: Consecutive\: Integer =\: x =\: 17}}$

$\small \dashrightarrow \sf\bold{\red{Second\: Consecutive\: Integer =\: x + 1 =\: 17 + 1 =\: 18}}$

$\therefore$ The two consecutive positive integers are 17 and 18 .