if a and alpha beta are the zeroes of the quadratic polynomial f(x)=ײ - 10x + 9, then find a quadratic polynomial whose zeroes are 1/a and 1/ alpha beta
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0
Answer:
Given: p(x)=x
2
+10x+30
So, Sum of zeroes =α+β=
a
−b
=
1
−10
=−10…(1)
=αβ=
a
c
=
1
30
=30…(2)
Product of zeroes Now, Let the zeroes of the quadratic polynomial be α
∧
=α+2β,β
′
=2α+β
Then, a
′
+β
′
=a+2β+2a+β=3α+3β=3(α+β)
α
′
β
′
=(α+2β)×(2α+β)=2α
2
+2β
2
+5αβ
Sum of zeroes =3(α+β)
Product of zeroes =2a
2
+2β
2
+5αβ
Then, the quadratic polynomial =x
2
−( sum of zeroes )x+ product of zeroes =x
2
−(3(a+β))x+2a
2
+2β
2
+5aβ
=x
2
−3(−10)x+2(a
2
+β
2
)+5(30){ from eq
n
(1)&(2)}
=x
2
+30x+2(a
2
+β
2
+2aβ−2aβ)+150
=x
2
+30x+2(a+β)
2
−4aβ+150
=x
2
+30x+2(−10)
2
−4(30)+150
=x
2
+30x+200−120+150
=x
2
+30x+230
So, the required quadratic polynomial is x
2
+30x+230
Answered by
1
Answer:
How rude gy u r !
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