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\$.

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

Option C

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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.

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

Option D

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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.

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

Option B

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

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

Option C

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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.

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

Option A