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18. Find the quadratic polynomial, whosezeroes are in the ratio 2:3 and their sumis 15​

Answer»

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


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