If $(x - k)$ is a common factor of $x^{2} + 3 x + a$ and $x^{2} + 4 x + b$ , then find the value of k in terms of a and b.

a + b

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a - b

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2 a + 3 b

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2 a - 3 b

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Solution

The correct option is B $a - b$
Given $x - k$ is a common factor of $x^{2} + 3 x + a$ and $x^{2} + 4 x + b$
Therefore,
$(k)^{2} + 3 k + a = 0$ and $(k)^{2} + 4 k + b = 0$
$⟹ k^{2} + 4 k + b = k^{2} + 3 k + a$
$k = a - b$

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2^{a} + 3^{b} = 17

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2 a - 3 b + 4 c .

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If ' $a$ ' and ' $b$ ' are the non-zero distinct zeros of $x^{2} + a x + b$ , then the least value of quadratic polynomial $x^{2} + a x + b$ is

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