Question

if A and B are the zeros of a quadratic polynomial such that a + b is equal to 24 and a minus b is equal to 8 find the quadratic polynomial having a and b as it zeros.verify the relationship between the zeros and coefficient of the polynomial.

Answer 1

Hello !

Since a+b = 24
a-b = 8
therefore, by elimination method,
a=16 & b=8

Now product of zeros = (16×8) = 128,
Since quadratic polynomial is x²-sumx + product,
therefore, quadratic polynomial will be ---
x² - 24x + 128

Now verification,
Sum of zeros = -(coefficient of x) ÷ (coefficient of x²),
16+8= -(24)÷1
24 = 24. proved,

Now, product of zeros = constant term ÷ (coefficient of x²),
16×8=128÷1
128=128,
hence, verified.


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