Question

Find the zero of the polynomial and verify the relationship between zero and the coefficent of zero

3x^2+5x-2​

Answer 1

+3x^2-5-2 is ur answer

Answer 2

Given :

• A polynomial 3x² + 5x - 2 .

To Find :

• Zeroes of the polynomial and verify the relationship between zero and the coefficent of zero .

Solution :

$\longmapsto\tt\bf{{3x}^{2}+5x-2}$

By Splitting Middle Term :

$\longmapsto\tt{{3x}^{2}+(6x-1x)-2}$

$\longmapsto\tt{{3x}^{2}+6x-1x-2}$

$\longmapsto\tt{3x(x+2)-1(x+2)}$

$\longmapsto\tt{(3x-1)\:(x+2)}$

• x = 1/3
• x = -2

So , 1/3 and -2 are the zeroes of 3x² + 6x - 2 ..

_______________________

Here :

• a = 3
• b = 5
• c = -2

Sum of Zeroes :

$\longmapsto\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\longmapsto\tt{\dfrac{1}{3}+\dfrac{(-2)}{1}=\dfrac{-5}{3}}$

$\longmapsto\tt{\dfrac{1-6}{3}=\dfrac{-5}{3}}$

$\longmapsto\tt\bf{\dfrac{-5}{3}=\dfrac{-5}{3}}$

Product of Zeroes :

$\longmapsto\tt{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{\dfrac{1}{3}\times\dfrac{-2}{1}=\dfrac{-2}{3}}$

$\longmapsto\tt\bf{\dfrac{-2}{3}=\dfrac{-2}{3}}$

HENCE VERIFIED