Question

find the sum of the zeroes of the polynomial x²+x+1​

Answer 1

$\maltese\:\large{{\pmb{\sf Solution:-}}$

○ Consider the zeroes of this equation as α and β

○ The sum of the zeroes is given by:-

$\\\leadsto\underline{\boxed{\sf \alpha+\beta=\dfrac{-b}{a} }}\bigstar$

○ where a and b are coefficient of x² and coefficient of x respectively

○ Now, substitute the values of a and b in the formula in order to get the sum of zeroes.

$\\:\implies\sf \alpha +\beta =\dfrac{-1}{1}$

$\\:\implies \boxed{\boxed{\sf \alpha +\beta = -1} }}\bigstar$

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Product of roots (zeroes):-

○ for any quadratic equation ax² + bx + c , we have 2 roots that can satisfy the equation.

○ product of those 2 roots can be calculated by : -

$\\\leadsto\underline{\boxed{\sf \alpha.\beta=\dfrac{c}{a}  }}\bigstar$

○ where, a and c are coefficient of x² and constant respectively.

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Answer 2

Given : Quadratic equation is x² - x + 1

To find : Sum of zeroes

Solution :

For every Quadratic equation, sum of zeroes can be expressed as - b / a where a is the coefficient of x² and b is the coefficient of x for a quadratic equation in variable x.

General form of quadratic equation is,

• ax² + bx + c = 0

In the given equation x² + x + 1,

• Coefficient of x², a = 1
• Coefficient of x, b = 1
• Constant term, c = 1

Applying the formula to find the sum of zeroes,

=> Sum of zeroes = - ( coeff.of x) / (coeff. of x²)

=> Sum of zeroes = - 1 / 1

=> Sum of zeroes = -1

So the sum of zeroes of the given quadratic equation is -1.

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