Question

find the zeroes of the quadratic polynomial xsquare+5x-6 and verify the relationship between the zeroes and the coefficient​

Answer 1

Answer:

Step-by-step explanation:

x²+5x-6=0

x²+6x-1x-6=0

x(x+6)-1(x+6)=0

(x+6)(x-1)=0                              

(x+6)=0                                 x-1=0

x= -6                                     x=1

∝+β= -b/a

-6+1 = - -5/1

    -5 = -5

∝β = c/a

-6×1 = -6/1

   -6 = -6

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The quadratic polynomial x² + 5x - 6.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The zeroes and verify the relationship between the zeroes and the coefficient.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We have p(x) = x² + 5x - 6

Zero of the polynomial p(x) = 0

So;

$\longrightarrow\sf{x^{2} +5x-6=0}\\\\\longrightarrow\sf{x^{2}+ 6x-x-6=0}\\\\\longrightarrow\sf{x(x+6)-1(x+6)=0}\\\\\longrightarrow\sf{(x+6)(x-1)=0}\\\\\longrightarrow\sf{x+6=0\:\:\:Or\:\:\:x-1=0}\\\\\longrightarrow\sf{\pink{x=-6\:\:\:Or\:\:\:x=1}}$

∴ The α = -6 and β = 1 are the zeroes of the polynomial.  

As the given quadratic polynomial as we compared with ax² + bx + c ;

• a = 1
• b = 5
• c = -6

So;

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

$\mapsto\sf{\alpha +\beta =\dfrac{-b}{a} =\dfrac{Coefficient\:of\:x}{Coefficient\:of\:(x)^{2} } }\\\\\\\mapsto\sf{-6+1=\dfrac{-5}{1} }\\\\\\\mapsto\sf{\pink{-5=-5}}$

$\underline{\green{\mathcal{PRODUCT\:OF\:THE\:ZEROES\::}}}$

$\mapsto\sf{\alpha \times \beta =\dfrac{c}{a} =\dfrac{Constant\:term}{Coefficient\:of\:(x)^{2} } }\\\\\\\mapsto\sf{-6\times 1=\dfrac{-6}{1} }\\\\\\\mapsto\sf{\pink{-6=-6}}$

Thus;

Relationship between zeroes and coefficient is verified .