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

Factorization of quadratic polynomials of theorem ax^(2)+bx+ca!=1

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

The sum and product of the zeroes an a quadratic polynomial P (x) = ax^(2) + bx +c are -3 and 2 respectively, Show that b+c = 5a.

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 both the zeroes of a quadratic polynomial ax^(2) + bx + c are equal and opposite in sign, then b is

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 ?

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 ?