Question

find a quadratic polynomial where zeroes are -4 and 3 and verify the relationship between the zeroes and the coefficients​

Answer 1

Answer:

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sum of zeroes= -4+3= -1

product of zeroes= -4*3= -12

quadratic polynomial= k(x^2 - sx + p)

= k(x^2 -(-1)*x + -12)

= k(x^2+ 1x -12)

taking LCM

k=1

1(x^2+1x -12)

the quadratic polynomial = x^2+1x-12 where k=1

verification of the relationship b/w zeroes and coefficients,

sum of zeroes= -1

also sum of zeroes= -(coefficient of x/coefficients of x^2)

= -(+1)/1 = -1

therefore, sum of zeroes = -(coefficient of x) / (coefficient of x^2)

product of zeroes= -12

also product of zeroes = constant term/ coefficient of x^2

= -12/1= -12

therefore, product of zeroes= constant term/ coefficient of x^2