Question

Question 7
Find the roots of the quadratic trinomial 4x2 = 14x + 8.

Answer 1

x = 4,-0.5

Explanation:

There are many methods to solve for the roots of a quadratic trinomial.

A simple method is to use quadratic formula which is :

x = ( -b ± √( b^2 - 4ac ) ) / ( 2a )

These a's, b's and c's represent the coefficients in the equations shown below

a
`x^(2)` + bx + c = 0

To solve for the roots we need to put our current equation in the form above :

4x^2 - 14x - 8 = 0

Then if we insert these numbers into the quadratic formula we get:

x = ( 14 ± √( 196 - 4(4)(-8) ) ) / ( 2(4) ) --->

x = ( 14 ± √(324 ) ) / ( 8 ) --->

x = (14 ± 18) ) / ( 8 )

Since there is a plus or minus sign, there will be 2 solutions

One being x = 32/8 = 4

Another being x = -4/8 = -0.5