Do this guys as fast as u can....wid full explanation..
Answers
Step-by-step explanation:
1.
Given two zeroes are 2,-2.
Therefore,
(x + 2)(x - 2) = x² - 4
Now,
x² - 4 is a factor of x⁴ + x³ - 34x² - 4x + 120.
Long division method :
x² - 4) x⁴ + x³ - 34x² - 4x + 120 ( x² + x - 30
x⁴ + 4x²
----------------------------------------
x³ - 30x² - 4x
x³ - 4x
-----------------------------------------
- 30x² + 120
- 30x² + 120
----------------------------------------------
0
Now,
By using division algorithm, we have
f(x) = g(x) * q(x) - r(x)
⇒ x⁴ + x³ - 34x² - 4x + 120 = (x² - 4)(x² + x - 30) + 0
= (x² - 4)(x - 2)(x² + 6x - 5x - 30)
= (x + 2)(x - 2)x(x + 6) - 5(x + 6)
= (x + 2)(x - 2)(x - 5)(x + 6)
Therefore,
The zeroes are 2, - 2, -6, 5
(2)
Given,
-4 is a zero of the polynomial.
So,
P(-4) = 0
Now,
Place x = -4 in the polynomial.
⇒ (-4)² - (-4) - (2k + 2) = 0
⇒ 16 + 4 - 2k - 2 = 0
⇒ 20 - 2k - 2 = 0
⇒ k = 9
Therefore,
The value of k = 9
(3)
Given equation is 4x² + 3x + 7
Here,
a = 4, b = 3, c = 7.
Sum of zeroes : (α + β) = (-b/a) = -3/4
Product o zeroes : (αβ) = (c/a) = 7/4
Now,
(1/α) + (1/β)
⇒ (α + β)/αβ
⇒ -3/7
Therefore,
(1/α) + (1/β) = -3/7
Hope it helps!
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