If alpha and beta are the zeroes of the polynomial 3x² – 2x – 7, then find the value of
(i) 1/alpha + 1/beta -2( alpha × beta )
(ii) alpha square + beta square
Answers
Step-by-step explanation:
According to the given question it is already given that - ''If one zero of the quadratic polynomial f(x)=4 x² - 8 k x + 8 x - 9 is negative''
So let the roots of this polynomial be as follows :-
⇒ α , - α { As per to given )
We already know what is the sums of roots , ( i.e ...)
\alpha + ( - \alpha ) =α+(−α)= coefficient of x / coefficient of x²
\alpha - \alpha = \frac{-8k+8}{4}α−α=4−8k+8 → ( As per to given )
0 = -2k + 20=−2k+2 → ( After simplifying )
2k-22k−2
k = \frac{2}{2} = 1k=22=1
Hence the value of k is 1
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⇒ Now let us put the value of k as 1 in the given polynomial - kx² + 3 kx + 2
⇒ So we get as follows ,
⇒1 x^{2} + 3 x + 21x2+3x+2
→ Now , we can find the zeroes of polynomial by spliting the middle term method for 1 x^{2} + 3 x + 21x2+3x+2 -
x^{2} + 3x + x = 0x2+3x+x=0
x^{2} + 2x+ x+ 2 = 0x2+2x+x+2=0
x ( x + 2 ) + 1 ( x + 2 ) = 0x(x+2)+1(x+2)=0
(x + 1 ) ( x+ 2) = 0(x+1)(x+2)=0
→ Now , let us find the alpha and beta for the following polynomial to get the final answer :-
x + 1 = 0x+1=0
x = - 1x=−1
→Alpha - α = -1
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Another Zero :-
x + 2 = 0x+2=0
x = -2x=−2
→Beta - β = -2
Hence the two zeroes are -1 and -2.
Step-by-step explanation:
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