Find a quadratic polynomial whose zeroes 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 is ax²+bx+c is

Where a = 1, b= -1 and c= -12

Substitute the values in the above equation we get

x– x – 12 = 0

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