Question

sum of zeroes of a polynomial p(x)= x² + 7x + 10 is_____​

Answer 1

Answer:

-7

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Answer 2

Solution :

We have quadratic polynomial p(x) = x² + 7x + 10 & zero of the polynomial p(x) = 0.

$\underline{\underline{\tt{Using\:\:by\:\:factorization\:\:method\::}}}$

$\mapsto\sf{x^{2} + 7x + 10=0}\\\\\mapsto\sf{x^{2} + 2x+5x + 10=0}\\\\\mapsto\sf{x(x+2) + 5(x+2) = 0}\\\\\mapsto\sf{(x+2)(x+5)=0}\\\\\mapsto\sf{x+2=0\:\:\:Or\:\:\:x+5=0}\\\\\mapsto\bf{x=-2\:\:\:Or\:\:\:x=-5}$

∴ α = -2 & β = -5 are the zeroes of the given polynomials .

Now;

$\underline{\mathcal{SUM\:OF\:THE\:ZEROES\::}}$

$\mapsto\tt{\alpha +\beta =\dfrac{-b}{a} =\bigg\lgroup\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}} \bigg\rgroup}\\\\\\\mapsto\tt{-2 + (-5) }\\\\\mapsto\tt{-2 -5}\\\\\mapsto\bf{-7}$

Thus;

The sum of the zeroes of a polynomials is -7 .