Question

find a quadratic if the sum and Product of whose Zeroes
are-2
and 5 respectively​

Answer 1

Answer:

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

Here

α = 2

β = -5

We know that

(1) Sum of the zeroes

⇒ α + β

⇒ 2 – 5

⇒ -3……………………………(1)

(2) Product of the zeroes

⇒ α × β

⇒ 2 × (-5)

⇒ -10……………………………(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 equations (1) and (2) we get

⇒ k[x2 + 3x – 10]

When k = 1 the quadratic equation will become

x2 + 3x – 10