Question

Determine the number of real solutions each quadratic equation has. y = 12x2 - 9x 4

Answer 1

ANSWER

The quadratic function,

$y = 12 {x}^{2} - 9x + 4$
has no real roots.


EXPLANATION

We use the discriminant,

$D = {b}^{2} - 4ac$

to determine the nature of the roots of a quadratic equation.


If we compare

$y = 12 {x}^{2} - 9x + 4$

to

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



Then

$a=12,b=-9,c=4$


We substitute these values in to the formula for the discriminant, to obtain,



$D = {( - 9)}^{2} - 4(12)(4)$


$D = 81 - 192$


This implies that,

$D = - 111 \: < \: 0$


Since the discriminant is zero, the quadratic function,


$y = 12 {x}^{2} - 9x + 4$

has no real roots.

Answer 2

  Find the Vertex of   y = 12x2-9x+4
   y = 2.313