Find the two other zeroes of x 4 + 2x3 – 13x2 – 12x + 21 . Zeroes are 2+√3,2-√3
Answers
Answer:
marry Christmas
Step-by-step explanation:
(xii) q(y)=7y2-
11
3
y-
2
3
ANSWER:
(i) We have,
f(x) = x2 − 2x − 8
f(x) = x2 + 2x − 4x − 8
f(x) = x (x + 2) − 4(x + 2)
f(x) = (x + 2) (x − 4)
The zeros of f(x) are given by
f(x) = 0
x2 − 2x − 8 = 0
(x + 2) (x − 4) = 0
x + 2 = 0
x = −2
Or
x − 4 = 0
x = 4
Answer:
(x) = x2 − 2x − 8
f(x) = x2 + 2x − 4x − 8
f(x) = x (x + 2) − 4(x + 2)
f(x) = (x + 2) (x − 4)
Step-by-step explanation:
(x) f(v)=v2+43–√v−15
(xi) p(y)=y2+35√2y−5
(xii) q(y)=7y2−113y−23
ANSWER:
anwer and some examples
The zeros of f(x) are given by
f(x) = 0
x2 − 2x − 8 = 0
(x + 2) (x − 4) = 0
x + 2 = 0
x = −2
Or
x − 4 = 0
x = 4
Thus, the zeros of f(x) = x2 − 2x − 8 are α = −2 and β = 4
Now,
and
Therefore, sum of the zeros =
Product of the zeros
= − 2 × 4
= −8
and
Therefore,
Product of the zeros =
Hence, the relation-ship between the zeros and coefficient are verified.
(ii) Given
When have,
g(s) = 4s2 − 4s + 1
g(s) = 4s2 − 2s − 2s + 1
g(s) = 2s (2s − 1) − 1(2s − 1)
g(s) = (2s − 1) (2s − 1)
The zeros of g(s) are given by
Or
Thus, the zeros ofare
and
Now, sum of the zeros
and
Therefore, sum of the zeros =
Product of the zeros
and =
Therefore, the product of the zeros =
Hence, the relation-ship between the zeros and coefficient are verified.
(iii) Given
We have,
h(t) = t2 − 15h(t) = (t)2 − (15−−√)2h(t) = (t + 15−−√) (t − 15−−√)
The zeros of are given by
h(t) = 0(t − 15−−√) (t + 15−−√) = 0(t − 15−−√) = 0t = 15−−√or (t + 15−−√) = 0t = −15−−√
Hence, the zeros of h(t) are α = 15−−√ and β = − 15−−√.
Now,
Sum of the zeros
and =
Therefore, sum of the zeros =
also,
Product of the zeros = αβ
and,
Therefore, the product of the zeros =
Hence, The relationship between the zeros and coefficient are verified.
(iv) Given
We have,
The zeros of are given by
Or
Thus, the zeros of are and.
Now,
Sum of the zeros = α + β
and, =
Therefore, sum of the zeros =
Product of the zeros = α × β
and, =
Product of zeros =
Hence, the relation between the zeros and its coefficient are verified.
(v) Given
We have,
The zeros of are given by
Or
Thus, The zeros of areand
Now,
Sum of the zeros = α + β
and,
Therefore, Sum of the zeros =
Product of the zeros
and
Therefore, The product of the zeros =
Hence, the relation-ship between the zeros and coefficient are verified.
(vi) Given
We have,
The zeros of g(x) are given by
Or
Thus, the zeros of are and.
Now,
Sum of the zeros = α + β
and =
Therefore, sum of the zeros =
Product of zeros = α × β
and =
Therefore, the product of the zeros =
Hence, the relation-ship between the zeros and coefficient are verify
I hope it's helpful for you