Question

Find a quadratic polynomial whose zeroes are –4 and 3 and verify the relationship between the zeroes and the coefficients.

Answer 1

I think answer might be helpful

x^2+12x-1=0

Answer 2

Answer:

Step-by-step explanation:

Let Alpha = -4 and Beta = 3.

Sum of zeroes = Alpha + Beta = -4 + 3 = -1

And,

Product of zeroes = Alpha × Beta = -4 × 3 = -12.

Therefore,

Required quadratic polynomial = X² - ( Sum of zeroes)X + Product of zeroes

=> X² - ( -1 ) X + ( -12 )

=> X² + X - 12.

_____________________________

P ( X ) = X² + X - 12

Here,

A = Coefficient of X² = 1

B = Coefficient of X = 1

And,

C = Constant term = -12

Relationship between the zeroes and Coefficients.

Sum of zeroes = Alpha + Beta = -4 + 3 = -1/1 = - ( Coefficient of X ) / ( Coefficient of X²).

And,

Product of zeroes = Alpha × Beta = -4 × 3 = -12/1 = Constant term / Coefficient of X².

hope it helps.................................................