Find the quadratic polynomial whose zeros are 3 and - 4.

Answer: x2 – x + 12

Let us assume quadratic polynomial be ax²+bx+c=0, where a≠0 and it’s zeroes be α and β.

Here

α = 3

β = – 4

We know that

(1) Sum of the zeroes

⇒ α + β = -b/a

⇒ 3 – 4 = -b/a

⇒ -1 = -b/a

b/a = 1…………………………..(1)

(2) Product of the zeroes

⇒ α × β = c/a

⇒ 3 × -4 = c/a

c/a = -12……………………………(2)

∴ The quadratic polynomial ax²+bx+c is k[x2 + (α + β)x + αβ]

Where k is constant.

k[x2 + (α + β)x + αβ]

From equation (1) and (2) we get

⇒ k[x2 – x + 12 ]

When k = 1 the quadratic equation will become

x2 – x + 12

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