Question

Find the quadratic polynomial whose zeros are ⅔ and -1/4. Verify the relation
between the coefficients and the zeros of the polynomial.

Answer 1

Answer:

12x²-5x-2

Step-by-step explanation:

α=⅔, β=(-¼)

Quadratic formula

=x²-(α+β)x+αβ

=x²-(⅔+(-¼))x+(⅔)(-¼)

=x²-(⅔-¼)x+(-1/6)

=x²-(8-3/12)x-1/6

=x²-(5/12)x-1/6

Multiply each term by 12

=x²×12-(5/12×12)x-1/6×12

=12x²-5x-2

Therefore, the quadratic polynomial is 12x²-5x-2.

Sum of zeroes=⅔+(-¼)=⅔-¼=8-3/12=5/12= -(-5)/12= -(Coefficient of x)/Coefficient of x²

Product of zeroes=⅔×(-¼)=(-2/12)= Constant term/Coefficient of x²

Hence verified