Question

Find the quadratic polynomial whose zeros are 2/3 and -1/4. Verify the relation between the coefficients and the
zeros of the polynomial.

Answer 1

Answer:

$12x^2-5x-2=0$

Step-by-step explanation:

The equation would be

$(x-\frac{2}{3})(x+\frac{1}{4})=0$

$(\frac{3x-2}{3})(\frac{4x+1}{4})=0$

$12x^2-5x-2=0$

Sum of roots = $\frac{2}{3} +\frac{-1}{4}=\frac{5}{12} =\frac{-b}{a}$

Product of roots = $\frac{2}{3}.\frac{-1}{4}=\frac{-1}{6}=\frac{-2}{12}=\frac{c}{a}$