Question

Find a quadratic polynomial whose zeros are 4 and 2​

Answer 1

Step-by-step explanation:

Answer: x²+2x–8

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

Here

α = -4

β = 2

We know that

(1) Sum of the zeroes

⇒ α + β

⇒ -4 + 2

⇒ -2……………………………(1)

(2) Product of the zeroes

⇒ α × β

⇒ -4 × 2

⇒ -8……………………………(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 -2x -8]

When k = 1 the quadratic equation will become

x2 -2x -8

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