Question

Find the zeroes of the quadratic polynomial 3x2+5x-2 and verify the relationship between the zeroes and the coeffients

Answer 1

Hope this helps you

Answer 2

Answer:

x= 1/3 and x=-2

Step-by-step explanation:

The given polynomial is

$P(x)=3x^2+5x-2$

Equate the given polynomial equal top zero to find the zeroes.

$P(x)=0$

$3x^2+5x-2=0$

Splitting the middle term, we get

$3x^2+6x-x-2=0$

$3x(x+2)-1(x+2)=0$

$(3x-1)(x+2)=0$

Using zero product property, we get

$3x-1=0\Rightarrow x=\frac{1}{3}$

$x+2=0\Rightarrow x=-2$

Therefore, the zeroes of the polynomial are -2 and 1/3.

If α and β are two zeroes of a polynomial $ax^2+bx+c$, then

$\alpha +\beta=-\frac{b}{a}$

$\alpha \beta=\frac{c}{a}$

For the given polynomial  α and β are -2 and 1/3 respectively.

$\alpha +\beta=-2+\frac{1}{3}\Rightarrow -\frac{5}{3}=-\frac{b}{a}$

$\alpha \beta=-2\times \frac{1}{3}\Rightarrow -\frac{2}{3}=\frac{c}{a}$

Hence verified.