Question

Find the zeroes of the following quadratic polynomials and verify the relationship

between the zeroes and the coefficients of 2xsquare +4x​

Answer 1

Step-by-step explanation:

2x² + 4x = 0

Let us take 2x as common

2x(x + 2) = 0

Case 1:-

If we take 2x to the LHS side:

x + 2 = $\frac{0}{2x}$

x + 2 = 0(because any number divided by 0 it will become 0)

x = -2

Case 2:-

If we take x + 2 to the LHS side:

2x = $\frac{0}{x+2}$

2x = 0

x = $\frac{0}{2}$(because any number divided by 0 it will become 0)

x = 0

Relationship between the zeros:-

α + β = $-\frac{b}{a}$

αβ = $\frac{c}{a}$

Here, α = -2, β = 0

a = 2(coefficient of x²)

b = 4(coefficient of x)

c = 0(constant term)

α + β = -2 + 0 = -2

$-\frac{b}{a}$= $\cancel{-\frac{4}{2}}$

= $-\frac{2}{1}$

= -2

$\implies{α + β = -\frac{b}{a}}$

αβ = (-2)(0) = 0

$\frac{c}{a}$ = $\frac{0}{4}$ = 0

$\implies{αβ = \frac{c}{a}}$

$\therefore{\underline{\underline{Verified}}}$