Question

Find the quadratic polynomial whose zeroes are 3 and 4​

Answer 1

Step-by-step explanation:

quadratic polynomial in terms of the zeroes (α,β) is given by

x2 -(sum of the zeroes) x + (product of the zeroes)

i.e, f(x) = x2 -(α +β) x +αβ

Now,

Given that zeroes of a quadratic polynomial are -3 and 4

Let α = -3 and β= 4

Therefore, substituting the value α = -3 and β= 4 inf(x) = x2 -(α +β) x +αβ, we get

f(x) = x2 - ( -3 + 4) x +(-3)(4)

= x2 - x -12

Thus, x2 - x -12 is the quadratic polynomial whose zeroes are -3 and 4.