Question

A two digit number is 4 times the sum of its digits and twice the product of its digits.Find the number.in quadratic equation

Answer 1

let the digits be x and y
let x is in the tens place then
it sill become 10x let y is in once place the it will become
1y
the original number be 10x+y
from the question
10x+y=4(x+y)
10x+y=4x+4y
10x-4x+y-4y=0
6x-3y=0
2x-y=0
2x=y. eq-1
again according to question
10x+y=2(xy)
substitute y=2x
10x+2x=2x(2x)
12x/2x=2x
6=2x
x=3
if x=3 then y=?
2x=y
y=6
the number is 36

Hope it helps you

Answer 2

Let the digit at tens and units place of the number be x and y respectively then, it is

Given that = 10x+y
10x+y=4(sum of digits) and 2xy
10x+y=4(x+y) and 10x+y=3xy
10x+y=4x+4y and 10x+y=3xy
6x-3y=0 and 10x+y-3xy=0
Y=2x and 10x+2x= 2xy(2x)
12x=4x2

4x2 - 12x =0
4x(x-3)=0
4x=0 or x=3

Here we have y= 2x=2×3=6
X=3 and y=6
Hence 10x+y -10×3+6=36

The required two digit number is 36