Find the zeroes of the following quadratic polynomials and verify the relationships between the zeroes and the coefficients of the polynomials:- (a): p(x) = 8x2 – 19x – 15; (b): q(x) = 4 3 x2 + 5x – 2 3 ; (c): f
Answers
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
Answer:
for first one ,
X=3,-5/8.
this is the answer