y-x-2-x-y-2x-2-x-m-and-y-kx-b-if-one-point-intersects-find-k-b-

Question Number 146611 by mathdanisur last updated on 14/Jul/21

y = x^{2} + x, y = 2 x^{2} + x + m a n d y = k x + b

i f o n e p o i n t i n t e r s e c t s, f i n d k \cdot b = ?

Answered by mr W last updated on 14/Jul/21

y = x^{2} + x = k x + b

x^{2} + (1 - k) x - b = 0

Δ = {(1 - k)}^{2} + 4 b = 0

y = 2 x^{2} + x + m = k x + b

2 x^{2} + (1 - k) x + m - b = 0

Δ = {(1 - k)}^{2} + 8 (b - m) = 0

4 b = 8 (b - m)

\Rightarrow b = 2 m

{(1 - k)}^{2} = - 8 m

1 - k = \pm 2 \sqrt{- 2 m}

k = - 1 \pm 2 \sqrt{- 2 m}

\Rightarrow k b = 2 m (- 1 \pm 2 \sqrt{- 2 m})

Commented by mathdanisur last updated on 14/Jul/21

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