Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and its Coefficient Sab First X square + 5 x + 6 second 6 x square minus 3

Answer 1

Hey user !!

Here is your answer !!

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1) x^2+5x+6

Split the middle term

x^2+3x+2x+6

By taking commons

x(x+3) +2(x+3)

x+2=0 , x+3=0

x=-2 , x=-3

Sum of zeroes ->-2-3=-5

-(coefficient of x)/(coefficient of x^2)

=-(-5)/1=+5

Product of zeroes ->-2(-3)=+6 ,

Constant term /coefficient of x^2

6/1=6

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2) 6x^2-3-7x

6x^2-7x-3=0 (By rearranging)

6x^2-9x+2x-3=0

By taking commons

3x(2x-3)+ 1 (2x-3)=0

3x+1=0 , 2x-3=0

3x=-1 , 2x=+3

x=-1/3 , x=+3/2

Sum of zeroes =(-1)/3 + (+3)/2 => (-2+9)/6=>7/6

-(Coefficient of x)/(coefficient of x^2)

-(-7)/6=>+7/6

Product of zeroes = -1/3(3/2) => -3/6 => -1/2

Constant term / coefficient of x^2

-3/6 => -1/2

Hope it is satisfactory :-)

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Answer 2

heya mate !!

here is your answer :-
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● your question is to find zeroes of the polynomial and verify the relationship between to zeroes and its coefficient.

:-- Your first question is :- x^2 + 5x + 6.

===> On solving quadratic polynomial we get,

===> x^2 + 3x + 2x + 6

===> x ( x + 3 ) + 2 ( x + 3 )

===> ( x + 2 ) ( x + 3 )

===> x = -2

===> x = -3

So, zeroes are -2 and -3

● Sum of the zeroes = ( -2 ) + ( -3 )

======> -5

● Product of the zeroes = -2 ( -3 )

======> 6
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Verify :-- ( x^2 + 5x + 6 )

a = 1
b = 5
c = 6

● Sum of the zeroes ==> -b/a

=====> -5/1

=====> -5

● Product of the zeroes ==> c/a

=====> 6/1

=====> 6

hence verified

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☆ Your second question is incomplete.
Please complete it !!
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hope it helps !!