Question

find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively:1/3 , 1/2​

Answer 1

•Question:

To find polynomial with its zeroes: 1/3 and 1/2.

•Answer:

$\longrightarrow$ Let,the quadratic polynomial be k( ax² + bx + c), where k≠0 and its zeroes be α and β.

•NOW,

$\longrightarrow$Sum of zeroes = 1/3 + 1/2

= 2+3 / 3×2

= 5/6

= -b/a

$\longrightarrow$Product of zeroes = 1/3 × 1/2

= 1/6

= c/a

Here, a=6, b= -5 and c=1.

By,comparing this values in k(ax² + bx +c), we get

$\huge\fbox{6x² - 5x + 1}$

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