Question

Factories
the following and verify the relation between zeros
and coefficient
2x square + 13 x + 20​

Answer 1

Answer:

relation between zeros

and coefficient

2x square + 13 x + 20

Answer 2

Given :

• Polynomial 2x²+13x+20.

To Find :

• Zeroes of the polynomial 2x²+13x+20.

Solution :

$\longmapsto\tt\bold{{2x}^{2}+13x+20}$

$\longmapsto\tt{{2x}^{2}+(8x+5x)+20}$

$\longmapsto\tt{2x(x+4)+5(x+4)}$

$\longmapsto\tt{(2x+5)\:\:(x+4)}$

• $x=\dfrac{-5}{2}$

• $x=-4$

So , -5/2 and -4 are the zeroes of polynomial 2x²+14x+20..

_______________________

Here :

• a = 2
• b = 13
• c = 20

Sum of Zeroes :

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

$\longmapsto\tt{\dfrac{-5}{2}+\dfrac{-4}{1}=\dfrac{-13}{2}}$

$\longmapsto\tt{\dfrac{-5-8}{2}=\dfrac{-13}{2}}$

$\longmapsto\tt\bold{\dfrac{-13}{2}=\dfrac{-13}{2}}$

Product of Zeroes :

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

$\longmapsto\tt{\dfrac{-5}{2}\times\dfrac{(-4)}{1}=\dfrac{20}{2}}$

$\longmapsto\tt{\cancel\dfrac{20}{2}=\cancel\dfrac{20}{2}}$

$\longmapsto\tt\bold{10=10}$

HENCE VERIFIED