Question

find a quadratic polynomial whose zeroes are -4/5and 1/3​

Answer 1

Answer:

» Question -

find a quadratic polynomial whose zeroes are -4/5and 1/3.

» Let alpha and beta be roots of the polynomial.

» We know that,

Form of quadratic equation =

${\pink{\boxed{x^2 - (\alpha +\beta)x + (\alpha × \beta)}}}$

» Given,

$\alpha = \frac{-4}{5}$

$\beta = \frac{1}{3}$

» by putting the values of alpha and beta.

$x^2-( \frac{-4}{5} +\frac{1}{3}) x +(\frac{-4}{5}× \frac{1}{3}) \\ \\ \\</p><p>= x^2 - [\frac{(-12 + 5)}{15}]x + \frac{-4}{15}\\ \\ \\</p><p>= x^2 - [\frac{-7}{15}]x + \frac{-4}{15}$

=${\pink{\boxed{x^2 +\frac{7}{15} x +\frac{-4}{15}}}}$