How one quadratic polynomial has two same zeros??
Answers
Answer:
For some quadratic polynomials, the two zeroes might be equal. For example, the polynomialp(x):x2−4x+4 p ( x ) : x 2 − 4 x + 4 can be rewritten as p(x):(x−2)2 p ( x ) : ( x − 2 ) 2 . Thus, we can say that this polynomial has the two zeroes: x=2,2, x = 2 , 2 , which happen to be identical.
Answer:
Hope it helps
Step-by-step explanation:
A Quadartic polynomial is a polynomial of degree 2.
e.g. A univariate quadratic polynomial will look some thing like this:
f(x) = ax^2 + bx + c , where x is the variable and a, b, c are constants and a isn’t equal to 0 else it will no more be quadratic
This what the function looks like
Now as you see that this quadratic function can touch the X axis at not more than two points (hence the degree 2).
If we equate it to zero, ax^2 + bx + c = 0 , then we call it a quadratic equation whose roots will be at most 2.
Let us say that the curve touches X-axis at points p, q
then ax^2 + bx + c = 0 can be written as k(x-p)(x-q) =0
Here, k is the factor and k is not equal to 0
p and q are the roots of the equation.
if p=q => the curve just touches the X-axis at 1 point
If the curve doesn’t touch the X-axis at all then p and q have no real values (imaginary roots of the form a+ib and a-ib)
In the graph above the equation ax^2 + bx + c = 0 is x^2-x-2 = 0
where a=1, b=-1 & c=-2
Solving this equation, as shown in the graph will have 2 roots -1 & 2
We may check it algebraically by factorizing x^2-x-2 = (x+1)(x-2)= 0
here k(x-p)(x-q) =0 has k=1, p=-1, q=-2