What is the difference between a factor of a quadratic equation and a zero of a quadratic equation?  ?

A quadratic EXPRESSION can be factorized while a quadratic EQUATION can be solved (for its zeroes).

For example, x² + 5x + 4 is a quadratic expression which has two factors (x+1) and (x+4).

But x² + 5x + 4 = 0 is a quadratic equation which is equivalent to (x+1)(x+4) = 0 which can then be solved to be x = −1 or x = −4 where −1 and −4 are the zeroes of the quadratic equation.

F(x) = ax^2 + bx + c you could sparkling up F(x) = 0 by potential of utilizing the quadratic equation formulation x = [-b +- sqrt(b^2 - 4ac)]/(2a) F(x) = a (x - r) (x - s) The ideas are x=r, s you will possibly be able to sparkling up the customary form by potential of utilizing the quadratic equation formulation or by potential of first changing into quadratic form. in case you could convert, then the two will supply an identical effect. however the conversion isn't constantly conceivable (or each and every each and every now and then may well be complicated). Write the equation of a parabola interior the form y = a quadratic expression in x If on the magnificent hand area, if the coefficient of x^2 is valuable, then formed up. in any different case formed down.

A factor of a quadratic function is (usually) a function of x which divides into the quadratic

Since (x-2)(x-3)=x^2-5x+6, both (x-2) and (x-3) are factors of x^2-5x+6 {WITHOUT =0}

The zeroes of x^2-5x+6=0 are the solutions of the equation, namely x=2 and x=3.

factor of the quadratic equation means you should find the factors say x-a or x-b like that

zero of the quadratic measn you should equate the factor of the quadratic to zero and that value when substitute in the equation should give the answer as zero

so x-a is a factor means

x-a=0

x=a for x=a the quadratic should be equal to zero

hope it is clear

(x+1)*(x-2) =0

in the above example (x+1) and (x-2) are factors of the equation. Factors when multiplied together give you the equation.

To find the zeros of the equation you set each factor to zero and solve for the value that makes it zero.

so x+1 = 0 results in x = -1 and -1 is a zero.

if you plot y = (x+1)(x-2) then the plot will cross the x axis at the zeros.