Question

Two positive, consecutive, odd integers have a product of 143.

Complete the equation to represent finding x, the greater intege

Answer 1

Explanation:

Answers:

k = 13The smallest zero or root is x = -10

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Work Shown:

note: you can write "x^2" to mean "x squared"

f(x) = x^2+3x-10

f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5

f(x+5) = (x^2+10x+25)+3(x+5)-10

f(x+5) = x^2+10x+25+3x+15-10

f(x+5) = x^2+13x+30

Compare this with x^2+kx+30 and we see that k = 13

Factor and solve the equation below

x^2+13x+30 = 0

(x+10)(x+3) = 0

x+10 = 0 or x+3 = 0

x = -10 or x = -3

The smallest zero is x = -10 as its the left-most value on a number line.

Answer 2

11,13

Explanation:

let the one of the number is x,then other of its consecutive odd number will be x+2

now their product will be

x(x+2)=143

i.e, x^2+2x=143

i.e, x^2+2x-143=0

i.e, x^2+13x-11x-143=0

i.e,x(x+13)-11(x+13)=0

i.e, (x+13)(x-11)=0

either x+13 =0,

or, x-11=0

i.e, x=11

it's positive number so x= -13 will be neglected

so the number will be 11

other one will be 11+2=13

✌️:)