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every quadratic equation is in the form
x^2-(a+b)x+ab
where a and b are zeroes!
given a =2/3 and b=-1/4
so equation is
x^2 -(2/3-1/4)x+2/3×-1/4
x^2-5x/12-1/6
= 1/12(12x^2-5x-2)..
now we have to verify
so we know already
that , a+b= 5/12
5/12=5/12
ab =-1/6
-1/6=-1/6
Answered by
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Alpha+beta = ,-b/a
-b/a = 2/3 (take first value)
-b/2=a/3
K=-b/2,K=a/3
b=-2K,a=3k
Alpha *beta =c/a
c/a=-1/4 (take second value)
c=-a/4
c=-3k/4 (put value of a)
Cubic equation is
ax^2+bx+c
3kx^2 -2kx-3k/4 (putting value of a b c)
K(3x^2-2x-3/4) (taking K comman)
Your quadratic equation is 3x^2-2x-3/4
Please mark it as brain list
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To Find: Find the polynomial
Solution:
formula of polynomial = x^{2}+(\alpha+\beta)x+\alpha\beta=0x2+(α+β)x+αβ=0
Where α = 2/3
β = -1/4
so putting values in formula:
x^{2}+(\frac{2}{3} -\frac{1}{4} )x+(\frac{2}{3}* \frac{-1}{4})=0x2+(32−41)x+(32∗4−1)=0
x^{2}+\frac{5}{12}x+\frac{-2}{12}=0x2+125x+12−2=0
12x^{2}+5x-2=012x2+5x−2=0
Hence the required expression is12x^{2}+5x-2=012x2+5x−2=0