Question

find the zeros of polinomical x²-3x-10​

Answer 1

Given :

• A polynomial x²-3x-10 .

To Find :

• Zeroes of the given Polynomial .

Solution :

$\longmapsto\tt\bf{{x}^{2}-3x-10}$

By Splitting Middle Term :

$\longmapsto\tt{{x}^{2}-(5x-2x)-10}$

$\longmapsto\tt{{x}^{2}-5x+2x-10}$

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

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

• x = -2
• x = 5

So , -2 and 5 are the zeroes of polynomial x²-3x-10 ..

_______________________

Here :

• a = 1
• b = -3
• c = -10

Sum of Zeroes :

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

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

$\longmapsto\tt{-3=-3}$

Product of Zeroes :

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

$\longmapsto\tt{-2\times{5}=\dfrac{-10}{1}}$

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

HENCE VERIFIED