Question

find the quadratic polynomial whose zeros are minus 2 and minus 5​

Answer 1

so let the zeros of polynomial be

α = -2

β = -5

so the formula of quadratic polynomial

α + β = $\frac{-b}{a}$

-2 + (-5) = $\frac{-b}{a}$

-7 = $\frac{-b}{a}$

so b = 7       and       a = 1

α × β = $\frac{c}{a}$

-2 × -5 = $\frac{c}{a}$

10 = $\frac{c}{a}$

so c = 10         and a = 10

Answer 2

Answer:

x² - 7x + 10

Step-by-step explanation:

Let the zeroes of the polynomial be α and β.

α = - 2 β = - 5

Now,

Sum of zeroes = α + β = (- 2) + (- 5)

α + β = - 7 ...(i)

Product of zeroes = αβ = (- 2)(- 5)

αβ = 10 ...(ii)

Now,

The required polynomial is :

= k [ x² + (α + β)x + αβ ]

= k [ x² + (- 7)x + 10 ]

= k [ x² - 7x + 10 ]

Put k = 1, we get

= x² - 7x + 10