Question

How one quadratic polynomial has two same zeros??​

Answer 1

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 2

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

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