If a quadratic polynomial f (x) is factorisable into linear distinct factors , then what is the total number of - Maths - Polynomials

Question

If a quadratic polynomial f (x) is factorisable into linear
distinct factors , then what is the total number of real and
distinct zeros of f (x) ?

also what is real zero and distinct zero ?

If a quadratic polynomial is the square of linear polynomial
then the two zers are coincident how ?
If f(x) is a polynomial such that f(a) f(b) < 0 , then what
is the number of zeros lying between a and b?

how plz explain ?

If y= f (x) and the lower parabola intersects at two points at
x axis and a point at y axis how many zeros are there ? two or
three? plz explain

are these questions very important ?

Harleen Birdi · Accepted Answer

(1) Let f(x) = (x â€“ a)(x â€“ b), where a â‰ b If a, b âˆˆ R, then f(x) must have two real and distinct zeros (2) Consider $f (x) = x^{2} - 4 x + 4$ $= (x - 2)^{2} = {[g (x)]}^{2} [where, g (x) = (x - 2), is a linear polynomial]$ Zero of g(x) is 2, so zeroes of f(x) are 2 and 2 i e , zeroes of f(x) are coincident (3) Let graph of f(x) be as

Let (a, (f(a)), (b, f(b)) be two points on f(x) such that f(a)f(b)< 0 Clearly, only one zero of f(x) namely c, between and b (4) If y = f(x) and the lower parabola touches each other, then number of zero will be 1

If y = f(x) and the lower parabola intersect each other, then number of zeros will be 2

However, number of zeros cant be 3 in any of the cases