Question

Find the zereos of the following quadratic polynomials and verify the relationship between the zereos and the co-efficients
1) 2x² - 9 - 3x
2) 2x² - 3 + 5x
3) 4u² + 8u
4) 3x² - x - 4

Answer 1

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Answer 2

$2x^2- 9 - 3x \\ 2x^2-6x +3x - 9 \\ 2x (x -3) +3 (x -3) \\ (2x +3)(x -3)$
Hence,
$x = \frac {-3}{2} and 3$
Varify :
Sum of roots = 3 + (-3/2) = -(-3)/2 =- coef. of x/coef. of x^2
products of roots = 3*(-3)/2 = -9/2 =constant/coef. of x^2

2) $2x^2 -3 + 5x \\ 2x^2 +6x -x -3 \\ 2x (x + 3)-(x +3)\\(x +3)(2x -1)$
Hence,
$x = \frac {1}{2} and -3$
Varify :
Sum of roots = 1/2 -3 = -5/2
Products of roots = 1/2 *(-3) = -3/2

3) $4u^2 + 8u \\ 4u (u + 2)$
hence,
u = 0 and -2
Varify :
Sum of roots = 0 + (-2) = -2
Products of roots = 0*(-2) = 0

4)$3x^2 - x -4 \\ 3x^2 -4x +3x -4 \\ (x + 1)(3x -4)$
hence,
x = -1 and 4/3
Varify:
Sum of roots = -1 + 4/3 = 1/3 = -(-1)/3
Products of roots = (-1)*(4/3) = -4/3