Question

find the quadratic polynomial whose zeros are in the ratio 2 ratio 3 and their sum is 15

Answer 1

Hii friend,

Ratio of the zero of the polynomial is 2:3.

Let X be multiply to both the numbers.

Then the zero becomes 2X and 3X.

According to question,

2X + 3X = 15

5X = 15

X = 15/5

X = 3.

Therefore,

One zeros = 2X = 2 × 3 = 6

And,

The another zero = 3X = 3 × 3 = 9

Let alpha = 9 and Beta = 6.

Sum of zeros = (Alpha + Beta) = (9+6) =15

Product of zeros = (Alpha × Beta) = 9 × 6 = 54

Therefore,

QUADRATIC POLYNOMIAL = X²-(Alpha + Beta)X + Alpha × Beta.

=> X²-(15X) + 54

=> X²-15X+54

Hence,

The Quadratic polynomial = X²-15X+54

HOPE IT WILL HELP YOU.... :-)

Answer 2

let zeoes are 2x and 3x and sum is 15 ... 2x + 3x =15
5x= 15
x = 15/5= 3.
so, 2x =2* 3=6
3x=3* 3=9.
6 and 9 are zeoes....
Quadratic equation = x square - (6+9)x +6*9
= x square -15x + 54 is the required polynomial hope it helps