Find a quadratic polynomial whose zeroes are - 4 and - 5​.

Answer: x² + 9x + 20

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

Here

α = -4

β = -5

We know that

(1) Sum of the zeroes

⇒ α + β

⇒ -4 – 5

⇒ -9……………………………(1)

(2) Product of the zeroes

⇒ α × β

⇒ -4 × -5

⇒ -20……………………………(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 + 9x + 20 ]

When k = 1 the quadratic equation will become

x2 + 9x + 20

Method 2:

Zeroes of the given quadratic polynomial be -4 and -5, so

(x – (-4))(x – (-5)5)

(x + 4)(x + 5)

x2 + 5x + 4x + 20

x2 + 9x + 20

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