Question

If a and bare zeroes of a polynomial such that a+b=6 and ab=4 then write the polynomial

Answer 1

Sum of zeros = -b/a = 6/1
product of zeros = c/a = 4/1

so a = 1 b= -6 , c = 4

let polynomial = ax^2+bx+c=0

x^2-6x+4= 0 Answer

Answer 2

Appropriate Question :-

• if a and b are the zeroes of the polynomial such that a+b=-6 and ab=-4 then write the polynomial

Required Answer :-

• x² - 6x + 4.

Concept used here :-

• If S is the sum of roots of a quadratic polynomial and P is its product, the quadratic polynomial is given by x² - Sx + P.

• Here, S = 6 and P = 4.

Therefore, quadratic polynomial = x² - Sx + P

• ::=> x² - 6x + 4

Additional details :-

• The choice of variable is immaterial. I have chosen x, likewise, once could take it as y , t or anything else.

• Therefore, if we write polynomial as y² - 6y + 4 , it exactly same as x² - 6x + 4