If the HCF of the polynomials $x^{2} + p x + q$ and $x^{2} + a x + b is x + l$ , then their LCM is

(x + a - l) (x + l - p)

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(x - (l + a)) (x + l - p) (x + l)

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(x + a - l) (x + p - 1) (x + l)

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(x - l + a) (x - p + l) (x + l)

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Solution

The correct option is D $(x - l + a) (x - p + l) (x + l)$
Given polynomials are $(x^{2} + p x + q)$ and $(x^{2} + a x + b)$

HCF $= x + l$ ; LCM $= ?$ ( $∵$ $L C M \times H C F =$ product of poly.)

On dividing the above polynomials by $(x + l)$ we get the answer

$∴$ LCM $= Q_{1} \times Q_{2} \times H C F$

$= (x + (p - l)) (x + (a - l)) (x + l)$

$= (x + a - l) (x + p - l) (x + l)$

Suggest Corrections

Similar questions

If the ratio of the roots of the equation $x^{2}$ +px+q=0 be equal to the ratio of the roots of $x^{2}$ +lx+m=0. Then

(- \frac{m}{l})

p (x) = l x + m

p (x) = l x + m, x = - \frac{m}{l}

(x + l) (x + m) = x^{2} + 4 x + 2

l^{2} + m^{2}

(l - m)^{2}

l (m y + n z - l x) = m (n z + l x - m y) = n (l x + m y - n z),

\frac{y + z - x}{l} = \frac{z + x - y}{m} = \frac{x + y - z}{n} .

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