Question

The product of two consecutive odd integer is 63. represent in the form of quadratic equation

Answer 1

let the number be
$x + 1$
and
$x + 3$
now the equation
$(x + 1)(x + 3) = 63 \\ {x}^{2} + 4x + 3 = 63 \\ {x}^{2} + 4x - 60 = 0 \\ {x}^{2} + 10x - 6x - 60 = 0 \\ x(x + 10) - 6(x + 10) = 0\\ (x - 6)(x + 10) = 0$
so x may be 6 or-10
so the no may be(7,9) or (-7,-9)

Answer 2

Answer:

Quadratic Equation - x ^ 2 + 2x - 63

Step-by-step explanation:

Since the consecutive odd number differ by 2, we may assume the numbers as follow:

First Consecutive Odd Number, m = ' x '

Second Consecutive Odd Number, n = ' x + 2 '

Hence on reading the question carefully we may derive the following relation :

m * n = 63

x * ( x + 2 ) = 63

Simplifying further,

x ^ 2 + 2x = 63

x ^ 2 + 2x - 63 = 0

x ^ 2 + 9x - 7x - 63 = 0

x ( x + 9 ) - 7 ( x + 9 ) = 0

( x + 9 ) ( x - 7 ) = 0

By zero product rule,

=> x + 9 = 0 OR => x - 7 = 0

=> x = - 9  OR => x = 7

Taking x = - 9,

First Consecutive Odd Number = - 9

Second Consecutive Odd Number = ( - 9 + 2 ) = - 7

Taking x = 7,

First Consecutive Odd Number = 7

Second Consecutive Odd Number = ( 7 + 2 ) = 9