Question

find the zeroes of polynomial x square +7x +10, and verify the relationship between the zeroes and the coefficients​

Answer 1

Given Quadratic Equation is

x² + 7x + 10

For finding the zeroes of the Quadratic Equation, we need to factorise it.

x² + 7x + 10 = 0

⇒ x² + 2x + 5x + 10 = 0

⇒ x(x + 2) + 5(x + 2) = 0

⇒ (x + 5) (x + 2) = 0

Now,

x + 5 = 0        or        x + 2 = 0

⇒ x = -5 or -2

For verifying the relationship between Zeroes and Coefficients,

Let,

α = -5

β = -2

For verifying the Sum of Zeroes,

$\bf{ \alpha + \beta = \dfrac{-b}{a}}\\\\\\\implies \sf{-5-2= \dfrac{-7}{1}}\\\\\\\implies \sf{-7 = -7}\\\\\bf{\underline{LHS = RHS}}\\\\\sf{Hence \: Verified}$

For verifying the product of Zeroes,

$\bf{\alpha \times \beta = \dfrac{c}{a}}\\\\\\\implies \sf{-5 \times -2= \dfrac{10}{1}} \\\\\\\implies \sf{10=10}\\\\\\\therefore \bf{\underline{LHS = RHS}}$

Hence Verified