Question

Given the Trinomial 5x^2- 2x-3, predict the type of solutions

Answer 1

Answer: Two distinct real roots.

Step-by-step explanation:

Given a quadratic equation $ax^2+bx+c=0$, we can predict the type of solution by calculating the Discriminant (D):

$D=b^2-4ac$

Identify a, b and c from $5x^2- 2x-3=0$.

$a=5\\b=-2\\c=-3$

Substitute into the formula of the Discriminant. Then:

$D=(-2)^2-4(5)(-3)\\D=64$

The discriminant obtained is greater than zero.

When $D>0$ the type of solution is: two distinct real roots.

Answer 2

ANSWER

The given trinomial will have two distinct real solutionss.

EXPLANATION

The given trinomial is

$5 {x}^{2} - 2x - 3$

When we compare to

$a{x}^{2} + bx + c$

, we have a=5, b=-2, c=-3

The discriminant of a quadratic trinomial helps us to predict the nature of the roots of a quadratic trinomial without necessarily solving for them.

We now use the discriminant

D=b²-4ac

to obtain,

$D= {( - 2)}^{2} - 4(5)( - 3)$

$D=4 + 60 = 64$

Since the discriminant is positive, the trinomial will have two distinct real solutions.