EduGoog

Solution of quadratic equations, Relation between roots and coefficients (only real roots to be considered). Practical problem on quadratic equations.

Quadratic Equations , Algebra

If α and β are the roots of the equation
$x^2 - 9x + 8 = 0$ (α > β) then find the value of
$α^2 - β^2$.

Option :
A. 63
B. 62
C. 65
D. None

If the sum of the roots of the equation $x^2 + 8x + 2 - k = 0$ is twice the product of the roots.
Then find k.

Option :
A. 2
B. 4
C. 8
D. 6

Find the values of k ε R subject to the following condition :
The sum of the roots of $3x^2 + kx - 2 = 0$ is 6.

Option :
A. 18
B. - 18
C. 12
D. 4

If the ratio of the roots of the equation $x^2 + 6x + k - 5 = 0$ is 3:5, then find the value of k.

Option :
A. $52/15$
B. $52/18$
C. $55/16$
D. $50/16$

If the roots of the equation $x^2 - 10x + k - 1 = 0$ are α and β and $α^3 + β^3 = 70$,
then find the value of k.

Option :
A. 32
B. 30
C. 16
D. 70