if α and β are zeroes of polynomial 2x2+ 5x + 1 find value of α+β and αβ
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Hi Mate!!
for a general quadratic equations ax² + bx +c = 0
![\alpha \: + \beta = - b \div a \: \: \: \\ \\ and \: \\ \\ \alpha \beta = c \div a \\ \\ \alpha + \beta \: = - 5 \div 2 \\ \\ and \: \\ \\ \alpha \beta \: = 1 \div 2 \\ \\ hope \: \: it \: \: helps \alpha \: + \beta = - b \div a \: \: \: \\ \\ and \: \\ \\ \alpha \beta = c \div a \\ \\ \alpha + \beta \: = - 5 \div 2 \\ \\ and \: \\ \\ \alpha \beta \: = 1 \div 2 \\ \\ hope \: \: it \: \: helps](https://tex.z-dn.net/?f=+%5Calpha++%5C%3A++%2B++%5Cbeta++%3D++-+b+%5Cdiv+a+%5C%3A++%5C%3A++%5C%3A++%5C%5C+++%5C%5C+and+%5C%3A++%5C%5C+++%5C%5C++%5Calpha++%5Cbeta++%3D+c+%5Cdiv+a++%5C%5C++++%5C%5C++%5Calpha++%2B++%5Cbeta++%5C%3A++%3D++-+5+%5Cdiv+2+%5C%5C++%5C%5C+and+%5C%3A++%5C%5C++%5C%5C++%5Calpha++%5Cbeta++%5C%3A++%3D+1+%5Cdiv+2+%5C%5C++%5C%5C+hope+%5C%3A++%5C%3A+it+%5C%3A++%5C%3A+helps)
for a general quadratic equations ax² + bx +c = 0
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11
Here is the answer
The given Equation is 2x^2 + 5x + 1 = 0
Comparing the given equation with
ax^2 + bx + c ,
We get the value of a , b, and c -
a = 2
b = 5
c = 1
Now ,
![\bf{\alpha + \beta = \frac{ - b}{a} } \bf{\alpha + \beta = \frac{ - b}{a} }](https://tex.z-dn.net/?f=+%5Cbf%7B%5Calpha+%2B+%5Cbeta+%3D+%5Cfrac%7B+-+b%7D%7Ba%7D+%7D)
![\bf{= \frac{ - 5}{2}} \bf{= \frac{ - 5}{2}}](https://tex.z-dn.net/?f=+%5Cbf%7B%3D+%5Cfrac%7B+-+5%7D%7B2%7D%7D+)
Now,
![\bf{\alpha \beta = \frac{c}{a} } \bf{\alpha \beta = \frac{c}{a} }](https://tex.z-dn.net/?f=+%5Cbf%7B%5Calpha+%5Cbeta+%3D+%5Cfrac%7Bc%7D%7Ba%7D+%7D)
![\bf{= \frac{1}{2}} \bf{= \frac{1}{2}}](https://tex.z-dn.net/?f=+%5Cbf%7B%3D+%5Cfrac%7B1%7D%7B2%7D%7D+)
Thanks!!
The given Equation is 2x^2 + 5x + 1 = 0
Comparing the given equation with
ax^2 + bx + c ,
We get the value of a , b, and c -
a = 2
b = 5
c = 1
Now ,
Now,
Thanks!!
Anonymous:
:Humpty Dumpty you are awesome:
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