Question

If X equal to -2 is a root of the equation 3 X^2 + 7 x + p = 0 find the value of k so that the roots of the equation X^2 + K(4 x + K - 1) + p = 0 are equal

Answer 1

x = - 2

3 x² + 7 x + p = 0

One root is - 2 .

So -2 will satisfy the value of x in the equation :

⇒ 3 ( -2 )² + 7 ( -2 ) + p = 0

⇒ 3 × 4 - 7 × 2 = - p

⇒ - p = 12 - 14

⇒ - p = - 2

⇒ p = 2

The equation x² + k ( 4 x + k - 1 ) + p has equal roots .

⇒ x² + k ( 4 x + k -1 ) + 2 = 0

⇒ x² + 4 k x + k² - k + 2 = 0

⇒ x² + 4 k x + k² - k + 2 = 0

Compare with ax² + bx + c = 0

a = 1

b = 4 k

c = k² - k + 2

b² = 4 ac

= 16 k² = 4 ( k² - k + 2 )

= 16 k² = 4 k² - 4 k + 8

= 12 k² = 8 - 4 k

= 4 k + 12 k² - 8 = 0

= 3 k² + k - 2 = 0

= 3 k² + 3 k - 2 k - 2 = 0

= 3 k ( k + 1 ) - 2 ( k + 1 ) = 0

= ( 3 k - 2 )( k + 1 ) = 0

Either k = - 1 or k = 2/3 .

Answer 2

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