Question

find a quadratic polynomial whose zeroes are 3 and -4 respectiveley

Answer 1

Let α=3
let β=-4
Now,
(α+β)= 3+(-4)
=-1
(α•β)=3*-4
=-12
So According to Quadratic formula
x^2-(α+β)x(α•β)
x^2+1x-12

Answer 2

Sum of the zeroes of a quadratic polynomial is given by
alpha + beta = -b/a
3 - 4 = -1 = -b/a
and product of zeroes
aplha × beta = -12 = c/a

Now let the polynomial be
f(x) = x² - (aplha + beta)x + alpha × beta
where alpha and beta denotes the zeroes of the given polynomial

On putting the values of sum and product of zeroes respectively we get

f(x) = x² + x -12 which is a required polynomial........

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