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Yogita Ingle 5 years, 6 months ago
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.
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Yogita Ingle 5 years, 6 months ago
To apply completing the square method, the quadratic equation must be in the form of
ax2 + bx + c = 0
Step 1 :
In the given quadratic equation ax2 + bx + c = 0, divide the complete equation by a (coefficient of x2).
If the coefficient of x2 is 1 (a = 1), the above process is not required.
Step 2 :
Move the number term (constant) to the right side of the equation.
Step 3 :
In the result of step 2, write the "x" term as a multiple of 2.
Examples :
6x should be written as 2(3)(x).
5x should be written as 2(x)(5/2).
Step 4 :
The result of step 3 will be in the form of
x2 + 2(x)y = k
Step 4 :
Now add y2 to each side to complete the square on the left side of the equation.
Then,
x2 + 2(x)y + y2 = k + y2
Step 5 :
In the result of step 4, if we use the algebraic identity
(a + b)2 = a2 + 2ab + b2
on the left side of the equation, we get
(x + y)2 = k + y2
Step 6 :
Solve (x + y)2 = k + y2 for x by taking square root on both sides.
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Abhishek Singh 5 years, 6 months ago
0Thank You