If one zero of the polynomial (3a2
– 9)x2
–10x +2a – 1 is reciprocal of the other, find the
value of k
Answers
Answer:
To find another zero of the polynamial x
2
−4x+1 , if one of them will be (2+
3
)
let consider two zeros α,β
α=2+
3
(given)
α+β=−
a
b
α+β=
1
−(−4)
(x
2
−4x+1comparingwithgenaralequationax
2
+bx+c,thena=1,b=−4,c=1)
α+β=4
fromequation(1)&(2)
α+β=4
2+
3
+β=4
β=4−(2+
3
)
β=4−2−
3
β=2−
3
To find another zero of the polynamial x
2
−4x+1 , if one of them will be (2+
3
)
let consider two zeros α,β
α=2+
3
(given)
α+β=−
a
b
α+β=
1
−(−4)
(x
2
−4x+1comparingwithgenaralequationax
2
+bx+c,thena=1,b=−4,c=1)
α+β=4
fromequation(1)&(2)
α+β=4
2+
3
+β=4
β=4−(2+
3
)
β=4−2−
3
β=2−
3
Explanation:
To find another zero of the polynamial x
2
−4x+1 , if one of them will be (2+
3
)
let consider two zeros α,β
α=2+
3
(given)
α+β=−
a
b
α+β=
1
−(−4)
(x
2
−4x+1comparingwithgenaralequationax
2
+bx+c,thena=1,b=−4,c=1)
α+β=4
fromequation(1)&(2)
α+β=4
2+
3
+β=4
β=4−(2+
3
)
β=4−2−
3
β=2−
3
Given;
To Find; One root is reciprocal to other
Solution; Since the roots are reciprocal of each other so the products of roots that is -b/a are one
1= 2a-1/3a^2-1
3a^2-1=2a-1
a(3a-2)=0
Hence the two possible values of a are 0 and 2/3