Factorization of quadratic polynomials of theorem `ax^2+bx+c` and `a != 1`

Factorize quadratic polynomial variable

The polynomial of type ax^(2)+bx+c , when a=0

Which of the following condition is correct for the graph of quadratic polynomial p(x) = ax^(2) + bx + c to be an upward parabola?

Which of the following condition is correct for the graph of a quadratic polynomial p(x) = ax^(2) + bx + c to be an upward parabola?

If the zeroes of the quadratic polynomial ax^(2) +bx +c , where c ne 0 , are equal, then

If x-(2)/(3) and x+3 are factors of the quadratic polynomial ax^(2)+7x+b , then find the values of a and b .

If both the zeros of the quadratic polynomial ax^2 + bx + c are equal and opposite in sign, then find the value of b.

If a,b,c in R, then for which of the following graphs of the quadratic polynomial y = ax ^(2) -2bx+ c (a ne 0), the product (abc) is negative ?

For the quadratic polynomial f(x)=ax^(2)+bx+c where a,b,c in R and a>=0. Match the condition column-1-1 with its no.of points of non- derivablity of y=|f(|x|)| in column-II