Find a quadratic polynomial whose sum and product respectively of

Juan Hewlett 2021-12-15 Answered
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given also find the zeoes of these polynomial by factorization
(-8/3),(4/3)
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Expert Answer

Durst37
Answered 2021-12-16 Author has 37 answers
Step 1 Given
(83),43
Step 2 Finding the zeroes
Sum of the zeroes =83
Product of the zeroes =43
p(x)=x2( of the zeroes)+(uct of the zeroes)
Then,
p(x)=x28x3+43
p(x)=3x28x+4
By factorization
3x28x+4=0
3x2(6x+2x)+4=0
3x26x2x+4=0
3x(x-2)-2(x-2)=0
(x-2)(3x-2)=0
x-2=0; 3x-2=0
x=2;x=23
x=2;23
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Maricela Alarcon
Answered 2021-12-17 Author has 28 answers
Step 1
Let the roots of a quadratic equation
ax2+bx=c=0 be α and β
So, α+β=ba=83...(1)
αβ=ca=43...(2)
ax2+bx+c=0
a(x2+bax+ca)=0
Step 2
x2(ba)x+ca=0
x2(α+β)x+αβ=0
Substitute (1) and (2) in above
x2(83)x+43=0
3x2+8x+4=0
The quadratic equation is 3x2+8x+4=0
Step 3
3x2+8x+4=0
3x2+2x+6x+4=0
x(3x+2)+2(3x+2)=0
(3x+2)(x+2)=0
x=23,x=2
The roots are 23,2
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