Question

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

Answer 1

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.

Answer 2

Answer: Two distinct real roots.

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.