Question

Find the zeroes of the following quadratic
polynomials & verify the relationship between
the zeroes & the coeff. of the polynomials :
a) p(x) = 8x^2-19x-15
​

Answer 1

Answer:

Given: (a): p(x) = 8x² – 19x – 15,  (b) q(x) = 4√3 x² + 5x – 2√3,

f(x) = 5x -4√3 + 2√3 x²

To find: The roots of given equations and verify them.

Solution:

So as we need to find the roots, lets write the first equation:

            p(x) = 8x² – 19x – 15

            formula to find roots are = -b ±√D/2a

            = 19 ± √((-19)² - 4(8)(-15))/ 2(8)

            = 19 ± √361  + 480 / 16

            = 19 ± √841 / 16

            = 19 ± 29 / 16

           48/16, -10/16

           x = 3, -5/8

Now solving the next equation, we get:

          q(x) = 4√3 x² + 5x – 2√3

          applying the same formula of roots:

          = -5 ± √((5)² - 4(4√3)( – 2√3))/ 2(4√3)

          = -5 ± √(25 + 96)/ 8√3

          = -5 ± √(121)/ 8√3

          = -5 ± 11/ 8√3

          = -16/8√3,  6/8√3

          x = -2/√3 , √3/4

Now solving the next equation, we get:

         f(x) = 2√3 x² + 5x - 4√3

         applying the same formula of roots:

         = -5 ± √25 - 4( 2√3)(- 4√3 )/2(2√3)

         = -5 ± √25 + 96 / 4√3

         = -5 ± 11 / 4√3

         = -16/4√3,  6/ 4√3

         x = -4/√3 , √3/2

Answer:

           So the roots of the equations are:

                   p(x) = 8x² – 19x – 15,   x = 3, -5/8

                   q(x) = 4√3 x² + 5x – 2√3,  x = -2/√3 , √3/4

                   f(x) = 5x -4√3 + 2√3 x² , x = -4/√3 , √3/2