Question

a quadratic polynomial whose zeroes are-2 and 5​

Answer 1

Step-by-step explanation:

METHOD 1:

x = -2

(x+2) is a factor of the Quadric equation

x = 5

(x-5) is a factor of the Quadric Equation.

Quadratic Equation: p(x) = (x + 2) (x - 5)

→ x² - 3x -10 =0

METHOD 2:

$\alpha = - 2 \\ \beta = 5 \\ general \: equation \\ {x}^{2} - ( \alpha + \beta )x \: + ( \alpha \beta ) = 0 \\ \\ sum \: of \: roots \: = \alpha + \beta = - 2 + 5 \\ \alpha + \beta \: = \: 3 \\ product \: of \: roots \: = \: \alpha \beta \: = \: ( - 2) \times 5 \\ \alpha \beta \: = \: - 10 \\ \\ putting \: these \: values \: in \: general \: Equation \: we \: get \\ {x}^{2} \: - \: (3)x \: + \: ( - 10) \: = \: 0 \\ {x}^{2} \: - \: 3x \: - 10 \: = \: 0$

Thanks!