Question

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

Answer 1

Answer:

THE QUADRATIC POLYNOMIAL IS P(x)= X^2-15X +54

Step-by-step explanation:

IT IS GIVEN THAT RATIO OF ZEROS OF THE POLYNOMIAL IS 2:3

LET THE TWO ZEROS ARE 2X AND 3X.

THE SUM OF ZEROS IS 15.

2X+3X=15

5X=15

X=3

THE VALUE OF X IS 3. SO THE ZEROS OF THE POLYNOMIAL IS 6 AND 9.

THE PRODUCT OF ZEROS IS 6X9=54.

THE QUADRATIC POLYNOMIAL IS DEFINED AS P(x)=X^2-MX+N

WHERE M IS THE SUM OF ZEROS AND N IS PRODUCT OF ZEROS.

SINCE SUM OF ZEROS IS 15 AND PRODUCT OF ZEROS IS 54, HENCE;

P(x)=X^2-15X+54

THUS THE QUADRATIC POLYNOMIAL IS P(x)=X^2-15X+54.

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