Question

State the number of real zeros and what they are for "3x^2+5x-2" pleas help me:'(

Answer 1

This can be solved by factoring.

First, set the expression equal to zero.

$3x^2+5x-2=0$

Then, find two the factors of  $ac$ whose sum is $b$.

$6, -1$

Split $b$ into these two factors.

$3x^2+6x-x-2=0$

Next, factor by grouping.

$3x(x+2)-1(x+2) = (3x-1)(x+2) = 0$

By the Zero Product Property, set each factor equal to zero.

$3x-1 = 0 \\ x = 1/3$

$x+2=0 \\ x = -2$

These are the solutions. The Complex Conjugate Root Theorem and the Fundamental Theorem of Algebra both state that, in essence, real and imaginary solutions come in pairs of two and every polynomial of degree $n$ has exactly $n$ complex roots, but real roots are also complex roots. That sounds confusing, but this just means that you're done. Your answers are -2 and 1/3. There are two real roots.