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Yogita Ingle 5 years, 7 months ago
For a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes, they are also referred to as roots of the polynomials, In general, we use to find the zeros of quadratic equations, to get the solutions for the given equation.
Zeros of a polynomial can be defined as the points where the polynomial becomes zero on the whole. A polynomial having value zero (0) is called zero polynomial. The degree of a polynomial is the highest power of the variable x.
- A polynomial of degree 1 is known as a linear polynomial.
The standard form is ax + b, where a and b are real numbers and a≠0.
2x + 3 is a linear polynomial. - A polynomial of degree 2 is known as a quadratic polynomial.
Standard form is ax2 + bx + c, where a, b and c are real numbers and a ≠ 0
x2+ 3x + 4 is an example for quadratic polynomial. - Polynomial of degree 3 is known as a cubic polynomial.
Standard form is ax3+ bx2 + cx + d, where a, b, c and d are real numbers and a≠0.
x3 + 4x + 2 is an example for cubic polynomial.
Similarly,
y6 + 3y4 + y is a polynomial in y of degree 6.
Posted by Jyoti Kharatmol 5 years, 7 months ago
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Yogita Ingle 5 years, 7 months ago
3x + 2ky - 2 = 0 ; 2x + 5y + 1 = 0
a₁ = 3 a₂ = 2
b₁ = 2k b₂ = 5
c₁ = -2 c₂ = 1
For parallel lines :-
a₁ = b₁ ≠ c₁
a₂ b₂ c₂
3 = 2k ≠ -2
2 5 1
15 = k
4
k ≠ -5
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Posted by Paras Kasliwal 5 years, 7 months ago
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Posted by Hema Anand 5 years, 7 months ago
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Yogita Ingle 5 years, 7 months ago
The prime factorization of 11008 is
2|11008
2|5504
2|2752
2|1376
2|688
2|344
2|172
2|86
43|43
1
11008=2×2×2×2×2×2×2×2×43
11008=2 × 8×43
The prime factorization of 7344 is
2|7344
2|3672
2|1836
2|918
3|459
3|153
3|51
17|17
1
7344=2×2×2×2×3×3×3×17
7344=2 × 4×3 × 3×17
Now, HCF=Product of the smallest power of each common
prime factor in the numbers.
HCF=2 × 4=16
LCM = Product of the greatest power of each prime factor,
involved in the numbers.
LCM=2 × 8×43×3 × 3×17=256×43×27×17=5052672
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