Question

Forming quadratic expression.Two consecutive odd numbers are such that their product is 35.find the numbers​

Answer 1

Numbers are 5 , 7

Explanation:

Forming quadratic equation and solving:

Let the two consecutive odd numbers be (2x + 1) and (2x + 3)

Their product = 35

(2x + 1)(2x + 3) = 35

Use FOIL method.

2x*2x + 2x*3 + 1*2x + 1*3 = 35

4x² + 6x + 2x + 3 = 35

Combine like terms

4x² + 8x + 3 = 35

4x² + 8x + 3 - 35 = 0

4x² + 8x - 32 = 0

Quadratic equation: 4x² + 8x - 32 = 0

Solving:

4x² + 8x - 32 = 0

Divide the entire equation by 2

`\sf (4)/(2)x^2 +(8)/(2)x - (32)/(2)=0`

2x² + 4x - 16 = 0

Sum = 4

Product = -32

Factors = 8 , (-4)

When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.

Rewrite the middle term

2x² + 8x - 4x - 16 = 0

2x(x + 4) - 4(x + 4) = 0

(x + 4) (2x - 4) = 0

2x - 4 = 0 {Ignore x +4 = 0 as it gives negative number}

2x = 4

x = 4/2

x= 2

2x + 1 = 2*2 + 1 = 5

2x + 3 = 2*2 +3 = 7

The numbers are 5 , 7