Hii please answer it don't sp
Answers
Answers:
Q.11] Find the zeroes of the polynomial in each of the following.
i) p(x) = x - 4
For finding the zero of the polynomial,
put p(x) = 0
x - 4 = 0
x = 4
Hence, the zero of polynomial is 4.
ii) Given polynomial is: g(x) = 3 - 6x
For finding the zero of the polynomial,
put g(x) = 0
3 - 6x = 0
=> 6x = 3
=> x = 3/6 = 1/2
Hence, the zero of polynomial is 1/2.
iii) q(x) = 2x - 7
For zero of polynomial,
put q(x) = 0
2x - 7 = 0
=> 2x = 7
=> x = 7/2
Hence, the zero of polynomial is 7/2.
iv) h(y) = 2y
For zero of polynomial,
put h(y) = 0
2y = 0
Hence, zero of polynomial is 0.
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Q.12] Find the zeroes of the polynomial.
p(x) = (x - 2)² - (x + 2)²
The given polynomial is in the form of (a)² - (b)²
Apply the formula:
a² - b² = (a + b) (a - b)
a = x - 2
[a² = (x - 2)²]
b = x + 2
[b² = (x + 2)²]
We get:
[(x - 2) + (x + 2)] [(x - 2) - (x + 2)] = 0
Simplifying the above equation,
(x - 2 + x + 2) (x - 2 - x - 2) = 0
2x × (-4) = 0
-8x = 0
x = 0
Therefore, p(x) = (x - 2)² - (x + 2)² = 0.
ANSWER:
★ 11 : Find the zeroes of the polynomial in each of the following
i) p(x) = x - 4
To get the zeroes put p(x) = 0
→ 0 = x - 4
→ x = 4
Hence , x = 4
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ii) g(x) = 3 - 6x
To get the zeroes put g(x) = 0
→ 0 = 3 - 6x
→ 6x = 3
→ x = 3/6
→ x = 1/2
Hence x = 1/2
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iii) q(x) = 2x - 7
To get the zeroes put q(x) = 0
→ 0 = 2x - 7
→ 2x = 7
→ x = 7/2
Hence, x = 7/2
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iv) h(y) = 2y
To get zeroes put h(y) = 0
→ 0 = 2y
→ y = 0/2
→ y = 0
Hence , y = 0
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★ 12: Find the zeroes of the polynomial
p(x) = (x - 2)² - (x + 2)²
Simplifying using
(a - b)² = a² + b² - 2ab
(a + b)² = a² + b² + 2ab
Putting p(x) = 0
→ 0 = x² + 2² - 2(x)(2) - [x² + 2² + 2(x)(2)
→ x² + 4 - 4x - x² - 4 - 4x = 0
→ - 8x = 0
→ x = 0/-8
→ x = 0
Hence , x = 0