Question

The quadratic equation ax² - 6x+a - 2 = 0 , a ≠ 0, has one root which is double the other. Let the roots be α and 2α. Hence find two equations involving α.

Answer 1

EXPLANATION.

→ Quadratic equation → ax² - 6x + a - 2 = 0

a ≠ 0.

→ one roots is double than other.

→ Let one roots be x and other roots be 2x

→ sum of zeroes of quadratic equation.

a + b = -b/a

x + 2x = 6/a

3x = 6/a

x = 2/a ....... (1)

→ products of zeroes of quadratic equation.

ab = c/a

x(2x) = a - 2 / a

2x² = ( a - 2 ) / a ........(2)

→ squaring equation (1) we get,

→ x² = 4/a²

→ divide equation (1) and (2) we get,

→ 2x²/x² = ( a - 2 )/a X a² / 4

→ 2 = ( a - 2 ) X a / 4

→ 8 = a² - 2a

→ a² - 2a - 8 = 0

→ a² - 4a + 2a - 8 = 0

→ a ( a - 4 ) + 2 ( a - 4 ) = 0

→ ( a + 2 ) ( a - 4 ) = 0

→ a = -2 and a = 4